Osmotic Collaborative Computing for Machine

2018 IEEE 4th International Conference on Collaboration and Internet Computing

Osmotic Collaborative Computing for Machine Learning and Cybersecurity Applications in Industrial IoT Networks and Cyber Physical Systems with Gaussian Mixture Models Emmanuel Oyekanlu Electrical and Computer Engineering Department, Drexel University, Philadelphia, Pennsylvania, USA. [email protected] Abstract—To implement machine learning algorithms and other useful algorithms in industrial Internet of Things (IIoT), new computing approaches are needed to prevent costs associated with having to install state of the art edge analytic devices. A suitable approach may include collaborative edge computing using available, resource-constrained IoT edge analytic hardware. In this paper, collaborative computing method is used to construct a popular and very useful waveform for IoT analytics, the Gaussian Mixture Model (GMM). GMM parameters are learned in the cloud, but the GMMs are constructed at the IIoT edge layer. GMMs are constructed using C28x, a ubiquitous, low-cost, embedded digital signal processor (DSP) that is widely available in many pre-existing IIoT infrastructures and in many edge analytic devices. Several GMMs including 2-GMM and 3-GMMs are constructed using the C28x DSP and Embedded C to show that GMM designs could be achieved in form of an osmotic microservice from the IIoT edge to the IIoT fog layer. Designed GMMs are evaluated using their differential and zero-crossings and are found to satisfy important waveform design criteria. At the fog layer, constructed GMMs are then applied for novelty detection, an IIoT cybersecurity and fault-monitoring application and are found to be able to detect anomalies in IIoT machine data using Hampel identifier, 3-Sigma rule, and the Boxplot rule. The osmotic collaborative computing method advocated in this paper will be crucial in ensuring the possibility of shifting many complex applications such as novelty detection and other machine learning based cybersecurity applications to edges of large scale IoT networks using low-cost widely available DSPs.

most analytics work are being shifted to network edges in a paradigm called edge computing. Challenges associated with edge computing are however numerous. Cost associated with deploying state of the edge analytic hardware are sometimes prohibitively expensive, and those costs can sometimes outweigh accruable benefits [3], [4], [5]. In edge computing, deploying multiple edge nodes can increase exposure footprints, and thus increases area exposable to cybersecurity attacks [3]. Thus, to reduce cost of edge computing, increasing the capacity of existing hardware, and finding new uses for existing hardware by making them more scalable [6], [7], [8], will be quite pivotal to successful deployment of IoT edgecomputing initiatives. Also, implementing distributed edge computing using multiple low-cost and readily available hardware can reduce incidence of single point of failure which can otherwise bring down a whole network right from the edge [9]. However, as earlier stated, edge computing, and by extension, distributed edge computing can increase footprint of a network, and thus increase areas of exposure of such distributed networks that are predisposed to cybersecurity attacks. Hence, the contribution of this paper is to propose and show examples by which existing low-cost IIoT hardware can be repurposed to participate in reliable and cybersecure edge computing. Specifically, a common, and readily available lowcost hardware is made to perform as a microservice hardware using a software defined osmotic computing approach by which different software types are used to implement different microservices between the edge and fog layer of an IIoT system. In addition, as the hardware is being made more scalable by repurposing it to perform microservice computing functions, methods of improving its cybersecurity are explored as well. The selected hardware is the Texas Instruments C28x, a DSP that has wide application in numerous large-scale engineering projects, industrial control, surveillance drones, aircraft cabin equipment, smart grid (SG) DC motors, industrial generators, and in estimated billions of machines and equipment [10], [11], [12], [13], [14] worldwide. Our contribution in this paper also shows that by using collaborative computing, important machine learning tasks such as novelty and outlier detection could eventually be made possible at edges of IIoT networks using widely available low-

Index Terms—osmotic computing, collaborative computing gaussian mixture model, embedded systems, machine learning, algorithms, hardware

I.

INTRODUCTION

Specificities of IIoT systems are quite stringent. For example, industrial control systems and similar Cyber Physical Systems (CPS) requires that delays resulting from end-to-end latencies to be confined within a few milliseconds [1], [2]. In addition, distances separating IIoT edge devices and their associated analytic platforms affects real-timeliness and thus, impact on reliability of resulting computations [2]. Cloud based IoT are quite useful for efficiently storing and processing information. However, to satisfy real-time constraints of IIoT, 978-1-5386-9502-9/18/$31.00 ©2018 IEEE DOI 10.1109/CIC.2018.00051

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microservice to prevent excessive data exchange and associated overheads. Edge constructed GMMs are shared with the fog layer device and used at the fog layer for outlier detection. The fog layer device is assumed to have more computing power than the C28x edge layer device [52]. The C28x DSP used in this work can be thought of as providing a microservice to the fog layer network by constructing the hardware based GMM at the network edge using GMM parameters that have been supplied from the cloud, and then, sharing constructed GMMs with the fog layer device. It is worthy to note that the fog layer device can also construct the GMMs using GMM parameters learned in the cloud. However, that low-cost IIoT edge hardware such as the C28x DSP can be used to construct GMMs increases the benefit of collaborative distributed computing. Thus, GMMs can be constructed at the edge using the low-cost C28x and those GMMs can be used by another layer of the network if the fog layer device is under cybersecurity attack, or if it is suffering from hardware failure. GMMs are constructed by the edge based C28x DSP in form of microservice using Embedded C programming language. To implement software delimited osmotic computing approach, a different software, Matlab, is used at the fog layer for outlier detection using the GMMs provided by the C28x DSP edge layer device. Gas turbine machine rotation results generated in [56] are used in this paper to show the workability of our methods for real industrial machines. Using the C28x, Embedded C based GMM,

cost, low-power hardware such as the C28x DSP. Novelty and outlier detections are quite useful in many IIoT operations in CPS systems. For example, outlier and novelty detection in remote oil installations is essential so that cybersecurity breaches like the Saudi Aramco oil installation attack that resulted to millions of USD in losses in August 2012 [15] can be prevented using existing infrastructure and intelligence based on IIoT edge analytics. Novelty detection involves using trained GMMs to decide whether a new observation is an inlier (belongs to the same distribution) or should be considered as different (outlier) [16]. The collaborative signal processing approach implemented in this paper was discussed in [17] [21], and it involves an assumption that big data in the IoT cloud have been used to learn and identify the parameters of the underlying Gaussian mixtures of some IIoT machine data that has been generated at the network edge but warehoused in the IoT cloud. Our contribution in this work now involves using the learned GMM parameters to construct associated IIoT machine GMM for the C28x DSP for possible use in novelty detection or other applications at edges of IIoT networks. This is a collaborative computing and signal processing approach, by which GMM training and learning is accomplished in the IIoT cloud, and the associated GMM is constructed at the edge of the IoT network using the lowmemory, low-cost DSP. Our entire contribution in this paper is as shown in the annotated diagram in Fig. 1. In Fig. 1, GMM construction at the edge of the network is treated as a

Sharing between edge and cloud: (1) GMM network parameters (mean and covariance) from cloud to edge. (2) Cybersecurity or fault alarm from edge to cloud Sharing between edge and fog: (1) Constructed GMM sent from edge to fog to improve collaboration and network resilience. (2) Machine condition & Cybersecurity issues determined at edge or fog layer using C28x based GMM constructed at the edge. Embedded C (Open Source, low computing resource)

Edge Layer

Software defined osmotic layer (1) Fog layer device can send alarm signal to edge layer (to actuate machine protection hardware) based on GMM analytics (2) It can also send alarm signal to cloud layer for further analytics and/or decision.

Software defined osmotic layer More computing resource (open source or proprietary software (e.g. Matlab) to improve on cybersecurity protection and fault monitoring

Embedded C

C28x based edge layer microservice device. (1) Use rotating machine mean and covariance learned from big machine data at cloud layer to construct system GMM. (2) Also, can use current rotating machine data to construct new GMM. (3) Send GMM to fog layer device. Can trigger instant alarm or defer to fog layer device for fault alarm decision

Fog Layer

Matlab etc.

Fog layer device: Operate closer to the edge to determine if rotating machine is faulty or under cybersecurity threat. Use GMM constructed at edge layer. Use multiple means (Boxplot, Hampel, 3Ǧ‹‰ƒ ”ules etc.) to determine existence or otherwise of (a) cybersecurity attack and/or (b) machine fault.

Enterprise level computing resource (open source (e.g. Python) or proprietary software)

Cloud Layer

Python etc.

Initial system or rotating machine parameters (mean, covariance) are learned (machine learning) in the cloud using big data generated by rotating machine situated at edge layer. GMM parameters are shared collaboratively with both fog and edge layer device

Fig.1. Illustration of the collaborative and osmotic computing approach for implementing edge-constructed GMMs using low-cost hardware and for improving IIoT Cybersecurity discussed in this paper

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decomposed into microservices which serve to improve modularity and make the whole network more robust against architecture erosion [29] - [33]. For example, in Fig. 1 the software defined osmotic layers include (1) the use of Embedded C to construct GMMs for the C28x DSP at the edge, (2) using Matlab (or other software) for machine fault monitoring and cybersecurity at the fog layer and (3) using Python (or other software), machine learning and big data to learn overall network parameters (means and covariance) and then, share the learned network parameters with the C28x DSP at the edge. Benefits of osmotic computing include: - Osmotic computing decomposes applications into microservices, thus leveraging microservices modularity to enhance system robustness against architecture erosion [29], [32]. - Microservices can be implemented using any desired programming language. This will facilitate ease of interoperability among different microservices, components, networks and different agents participating in osmotic computing [30]. - Osmotic computing allows adjustable configuration of hardware and software resources involved with computational tasks. This will facilitate involvement of low-cost, low-power devices commonly available in IoT systems [33]. - Osmotic computing due to dynamism in task allocations will facilitate load balancing, network decongestion, optimized communication spectrum use, reduced network latency, reliability and resource availability [30], [33]. Due to these benefits, it will be beneficial to hybridize and apply collective benefits of collaborative and osmotic computing in IIoT.

different rules of implementing cybersecurity and machine fault monitoring including Hampel identifier, 3Ǧ‹‰ƒ and boxplot rules are implemented for the gas turbine machine and their results compared. Our contribution reported in this paper is the first known direct GMM design for the ubiquitous C28x DSP. Since we use Embedded C, which always interface directly with hardware to construct the GMMs, our approach is more suitable for resource-constrained hardware at IoT edges, and our approach is different from the computationallyintensive state of the art approach, in which needed functions and waveforms such as the GMMs are always sourced from numerical computing toolboxes such as R and Matlab [22]. In this paper, we also discuss the benefits of osmotic computing and its applications in IIoT collaborative computing, in CPS, and in other engineering systems. In literature, several other authors have worked on the problem of creating hardware based GMM waveforms. In [23], authors report on the creation of a fully pipelined hardware based design for GMMs, however, the method outlined is only suitable for cloud based infrastructure and is not a workable model for resource constrained hardware at IoT edges. In [24], authors show the construction of approximate Gaussian waveform using the C28x DSP. It was proven that the hardware based approximate Gaussian fits a Matlab based normal distribution up to the 95% confidence interval. In [25], authors report on methods by which a VLSI based implementation of GMMs may be possible, however, as discussed in [26] using FPGAs, VLSI and ASIC circuits will lead to significant cost overlay when compared to implementation based on DSP circuits. In [27], authors report on using Vote Count circuit for hardware-based implementation of GMMs, however as discussed in [28], Vote Count circuit based algorithm implementation could have time complexity of Ɉ(n), and this will not be suitable for IIoT computing and edge analytic applications. The remaining part of this paper is as follows. In Section II, benefits of osmotic computing are discussed. The Expectation Maximization (EM) algorithm and GMM are briefly reviewed in Section III. Section IV presents a discussion of our method of constructing GMMs in this paper. Two-components (2-GMM) and three-components (3-GMM) GMMs are constructed from variable-frequency sine waves constructed for the C28x DSP. Section V presents an analysis of constructed GMMs using differential and zero-crossing criteria. Section VI shows how the GMM constructed at the edge using C28x DSP could be used at the fog layer for machine fault monitoring and for cybersecurity applications. Section VII is conclusion of the paper. II.

III.

BRIEF REVIEW ON GMM AND THE EXPECTATION MAXIMIZATION ALGORITHM

GMM is a linear superposition of several Gaussians each having its own mean and covariance. It is a method of fitting multiple Gaussians to a set of data that possibly have several dimensions. GMM is a probabilistic model that assumes all data points are generated from a mixture of Gaussian distributions with unknown parameters [16], [18], [34], [35]. The GMM model is always derived after using an appropriate algorithm, such as the EM algorithm to learn the underlying data distribution, which will consist of the means and covariances of the data points. In practice, learning underlying data distributions that eventually generates the Gaussian mixtures is generally accomplished in the cloud or data centers where abundant computing resources exists. The EM algorithm is a very popular algorithm for learning the data and fitting the parameters of the underlying distribution of a set of data, and its result after several iterations of its two steps which consists of the expectation (E-Step) and maximization (MStep) is the GMM. In using the EM algorithm, the mean of the data (Ɋ௞ ), the covariance (ᎂ௞ ) and the mixing coefficient (ߨ௞ ), are first initialized, and the initial value of the log likelihood is evaluated. For a D dimensional data set, k = 1......K Gaussians,

BENEFITS OF OSMOTIC COMPUTING

In osmotic computing, software defined osmotic layers are used to improve on performance of communications among microservices from edge to cloud and vice versa. Osmotic computing is an enabling architecture through which several hardware can participate in collaborative network computing according to their respective hardware strength and specification. Applications in osmotic computing are

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and n = 1…......N data points, Ɋ௞ is K means, each having a vector of length D and ᎂ௞ is K covariance matrices, each having size D x D. If we let P (‫ݔ‬௡ ) be model probability at ‫ݔ‬௡ , and P(k|n) be K probabilities for each data point, then the model probability could be represented as

C28x DSP using Embedded C. Needed parts of sine waves that represents different Gaussian shapes are then clipped and stored in the C28x DSP lookup table (LUT) [24]. Clipped signals are then fetched from the C28x LUT, sequenced, and concatenated together [37] - [40] (using Embedded C) to generate different 2-GMM and 3-GMM models for the C28x DSP. The method of signal clipping, sequencing and concatenation used in this paper is as illustrated in Fig. 2. In Fig. 2, to construct a Gaussian distribution having data values x of size 90 (with samples varying from 0 to 180 in steps of 2), with mean (μ) = 95, and variance (ߪ) = 30 as parameters (Fig. 2a), a sine wave of frequency 2.6 Hz and sampling frequency (fs) 90 Hz is created (Fig. 2b). In Fig. 2a, sample values x of the Gaussian distribution ([0: 2: 180]) results to a Gaussian distribution with amplitude 0.0139. The same amplitude value, (0.0139) is selected for the sine wave in Fig. 2b. The selected sine wave input frequency (2.6 Hz), fs, and amplitude (0.0139) ensures that the positive half cycle part (half sine) will approximate the needed Gaussian distribution with a low mean square error (MSE) as discussed extensively in [24]. The sine wave input frequency and fs are heuristically adjusted until the desired Gaussian waveform is achieved. The clipped positive half cycle part is shown in dashed block part in Fig. 2b, and resulting clipped waveform is shown in Fig. 2c. Similarly, to create another Gaussian waveform with mean (μ) = 170, variance (ߪ) = 14, and data samples x values varying from 110 to 230 in single step shown in Fig. 2d, an inverted sine wave with frequency 4.6 Hz, fs = 98 Hz and amplitude 0.0285 which is equal to the Gaussian waveform amplitude is created and shown in Fig. 2e. The final clipped part approximating the needed Gaussian waveform is shown in Fig. 2f. A concatenation of the Gaussian waveform marginals of Fig. 2c and Fig. 2f with no overlapping priors results to the GMM waveform shown in Fig. 2g. The C28x DSP that is used as a case study in this paper is the core processor of the TMS320C2000 powerline communication (PLC) modem that is designed for use at the low-voltage end of the smart grid (SG), a CPS [41]. This C28x DSP is selected since modems are always part of many available generic edge-analytic devices in IoT networks [37], [42], [43]. Also, the C28x DSP that is used is part of a SG PLC modem, and it is selected as a case study since SG is an integral part of IoT networks [44]. The Embedded C programming interface through which the sine waves and the n-GMM models are constructed is the Texas Instruments Code Composer Studio (CCS). CCS is a wellknown programming interface for real-time DSPs [38]. The experimental setup is as shown in Fig. 3. Using Embedded C frees the programmer from having to learn platform specific assembly language [39], [40. It also frees the programmer from having to use compute intensive numerical toolboxes such as R and Matlab toolboxes [22], thus enhancing benefits of osmotic collaborative computing by allowing low-cost DSPs to participate in collaborative computing using low-level programming language (Embedded C). Examples of multicomponent GMMs constructed for the C28x DSP in CCS environment using Embedded C with signal processing method described in Fig. 2 are shown in Fig. 4 and Fig. 5.

P (‫ݔ‬௡ ) = ᎂ௞ N (‫ݔ‬௡ | Ɋ௞ ǡ ᎂ௞ ) ߨ௞ ………….……………….……..(1) and the underlying Gaussian distribution N (x | μ, ‫ )گ‬in (1) could be represented as N(x | μ, ‫= ) گ‬

ଵ ಾ భ  ଶఒ మ ୢୣ୲ ᎂమ

ଵ

exp[- ሺ‫ ݔ‬െ Ɋሻᎂିଵ ሺ‫ ݔ‬െ Ɋሻ]……(2) ଶ

In the E-Step, by using the current values, the responsibilities, i.e., the probabilistic assignments of individual points to model is calculated. This leads to P(k|n) =

ேሺ௫೙ ȁஜೖ ǡᎂೖ ሻሺగೖ ሻ ௉ሺ௫೙ ሻ

………………………………….(3)

Then follows the M-Step. In the M-Step, the GMM is reestimated using refined assignment points from the E-Step. This will generate Ɋ෤௞ = ᎂ௡ P(k|n) ‫ݔ‬௡ / ᎂ௡ P(k|n) …………......…………… (4) ᎂ෨௞ = ᎂ௡ P(k|n) ሺ‫ݔ‬௡ െ  Ɋ෤௞ ሻ ٔ  ሺ‫ݔ‬௡ െ  Ɋ෤௞ ሻ/ ᎂ௡ P(k|n) ......(5) ߨ෤௞ =

ଵ ே

ᎂ௡ P(k|n)

where ٔ ݅݊(5), is a simplification that the covariance and have a Kronecker delta structure. After the M-Step, the loglikelihood is evaluated, leading to ln P (š୬ ȁɊǡ ᎂǡ ߨ) = σே ௡ୀଵ ݈݊ { ᎂ௞ N (‫ݔ‬௡ | Ɋ௞ ǡ ᎂ௞ ) ߨ௞ } ...........(6) If the log likelihood is evaluated, and there is no convergence, then the algorithm will return to the E-Step [18], [34], [35]. IV.

EXPERIMENTAL SETUP AND RESULTS

In this paper, it is assumed that the EM algorithm or any other suitable algorithm have been implemented in the cloud and the parameters and structure of the associated GMM have been identified [17] - [21]. Our accomplishment in this paper include finding suitable edge-analytic method by which resulting GMMs can be constructed for the widely available C28x DSP without using a numerical computing toolbox such as toolboxes from R or Matlab. The main reason for doing this is to make collaborative and osmotic computing possible using the widely available C28x DSP for GMM construction at the edge while the big data that have been used to train and identify parameters of the GMM remains in the cloud. This is a collaborative computing and signal processing approach that supports osmotic microservices, and thus optimize application integration in resource-constrained IoT networks, while using available infrastructure that are amenable to scalability. Towards this end, various GMMs are constructed for the C28x DSP using Embedded C in real-time DSP programming environment. The signal processing method adopted is first to construct sine waves that have different frequencies for the

329

Fig. 2c

Fig. 2b

Fig. 2a

Fig. 2f

Fig. 2g

Fig. 2e

Fig. 2d

Fig.2. Illustration of the method of creating GMMs from clipped parts of sine waves of varying frequencies discussed in this paper

V.

Gaussian distribution be N (x | μ, ‫ )گ‬which can also be represented as

RESULT EVALUATION

It is always desired that GMMs should have distinct Gaussian mixtures after the iteration of EM or any other algorithm selected for learning the parameters of the training data. However, GMMs sometimes have the problem of mixture identifiability when the mixture contains numerous Gaussian components [45], [46], [47]. This problem may sometimes be due to the underlying data structure or the fact that EM algorithm sometimes does not reach the global optimum before convergence [34]. The problem of GMM identifiability is given extensive coverage in [45], where it is shown that the non-identifiability of a mixture of Gaussians is relatable to the fact that covariances of a mixture of Gaussians is the same as their second derivative. Hence, the differential and the inflections points (shown in Fig. 2a for a Gaussian) of a mixture of Gaussian components may not be identifiable after the second derivative since the Gaussian components will then be covarying. Specifically, let the density of a multivariate

f(x) =

ଵ

ଵ భ

ሺξଶఒሻ೏ ȁᎂȁమ

exp[െ ሺ‫ ݔ‬െ Ɋሻᎂିଵ ሺ‫ ݔ‬െ Ɋሻ]..................(7) ଶ

The first and second derivatives of the GMM w.r.t the mean are డ௙ሺ௫ሻ డஜ

=െ

ଵ ೏

ଵ

భ

൫ξଶఒ൯ ȁᎂȁమ

exp[- ሺ‫ ݔ‬െ Ɋሻᎂିଵ ሺ‫ ݔ‬െ Ɋሻ](ᎂିଵ ሺ‫ ݔ‬െ Ɋሻሻ ଶ

(8) డమ ௙ሺ௫ሻ

=

డஜమ

ଵ

ଵ భ

ሺଶξଶఒሻ೏ ȁᎂȁమ ் ିଵ

ሾെᎂିଵ ൅ ᎂିଵ ሺ‫ ݔ‬െ Ɋሻሺ‫ ݔ‬െ Ɋሻ் ᎂିଵ ሿ

exp[െ ሺ‫ ݔ‬െ Ɋሻ ᎂ ሺ‫ ݔ‬െ Ɋሻ]...........................................(9) ଶ

The first derivative of (7) w.r.t the covariance ‫ گ‬is డ௙ሺ௫ሻ డᎂ

USB cable

ଵ ଶ

Code Composer Studio

=

ଵ భ

ሺଶξଶఒሻ೏ ȁᎂȁమ ் ିଵ

ሾെᎂିଵ ൅ ᎂିଵ ሺ‫ ݔ‬െ Ɋሻሺ‫ ݔ‬െ Ɋሻ் ᎂିଵ ሿ exp[െ

ሺ‫ ݔ‬െ Ɋሻ ᎂ ሺ‫ ݔ‬െ Ɋሻ]....................................................(10)

Direct comparison of (9) and (10) reveal that డమ ௙ሺ௫ሻ డஜమ

C28x DSP

Fig. 3. C28x DSP is embedded into generic IoT edge device like the TMS320C2000 powerline communication modem

330

ൌʹ

డ௙ሺ௫ሻ డᎂ

....................................................................(11)

Fig. 4. Two component GMM (2-GMM) constructed for the C28x IoT DSP. The Gaussian shapes are created from clipping from sine waves of different amplitudes, frequency and sampling frequency stored in C28x DSP LUT

The resulting 2-GMM and 3-GMM graphs are shown in Fig 6 and Fig. 7. The first and second derivatives are then evaluated with Matlab and plotted as shown in Fig. 8 to Fig. 11. According to [45], the 2-GMM must produces four zero crossing after the second derivative since n = 2 in the case of 2-GMM. Likewise, the 3-GMM must produce six zero crossings after the second derivative. The first derivative of 2GMM produce three zero- crossings as shown in Fig. 8 while its second derivative produces the required four zero crossings as shown in Fig. 9. For the 3-GMM, its first derivative yields five zero crossings (Fig. 10) while its second derivative results to six zero crossings (Fig. 11). This signifies that the Embedded C based method of clipping, concatenation and sequencing to produce GMMs for the widely available C28x DSP used as a case study in this paper works, and constructed GMMs may be deployed for further uses such as novelty detection at the edge of IoT networks.

Fig. 5. Three component GMM (3-GMM) constructed for the C28x IoT DSP. The Gaussian shapes are created from clipping from sine waves of different amplitudes, frequency and sampling frequency stored in C28x DSP LUT

The implication of (11) is that the inflection points of the GMM may not readily be separable or identifiable after the second derivative since the means of separate Gaussian mixture that constitute the GMM may not be identifiable. A possible solution to the problem of identifiability of the Gaussian components is discussed in [45]. In [45], it is discussed that a Gaussian have two inflection points, and this will cause its second derivative to produce two zero crossings. When n Gaussians are linearly combined as it is in the case of n-GMM construction considered in this paper, then the second derivative of the resulting GMM must have at most 2n zero crossings. To evaluate the 2-GMM and 3-GMM constructed for the C28x DSP considered in this work, the number of zerocrossings of constructed GMMs are examined. To accomplish the examination, 133 samples of each of the constructed GMMs in Fig. 4 and Fig. 5 are exported to Matlab from C28x CCS using Excel.csv format. The GMMs are then reproduced in Matlab by scaling down their amplitudes by two-order of magnitudes as discussed in [48] and [49].

VI. OSMOTIC COLLABORATIVE COMPUTING APPLICATION FOR IIOT MACHINE FAULT MONITORING AND CYBERSECURITY APPLICATIONS As earlier stated, the C28x DSP is deployed in estimated billions of applications in several industries worldwide [10], [13], [50], [51]. In this paper, the C28x DSP is repurposed to be an IIoT edge GMM generator by using Embedded C to program a generic IIoT edge device, i.e., a TMS320C2000 C28x PLC modem. In this section, the GMM constructed for the TMS320C2000 C28x edge device is provided as a microservice and shared with the IIoT fog layer for fault monitoring and for IIoT cybersecurity application. To show the C28x as a microservices device that can participate in osmotic computing in IIoT systems, another software, different from Embedded C is used at the fog layer to process the GMM samples supplied by the C28x DSP. It is assumed in this paper

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Fig. 12. Gas turbines are used extensively in several industries such as in CHP power generation and in aircraft engines.

Fig. 6. Two component GMM of Fig. 4 Fig. 7. Three component GMM of Fig. 9 reproduced with Matlab by exporting GMM reproduced with Matlab by exporting GMM samples from C28x DSP to Matlab samples from C28x DSP to Matlab

Fig. 8. 1st derivative of the 2-GMM showing 3 zero crossings

Fig.10. 1st derivative of the 3-GMM showing 5 zero crossings

turbine is obtained from [56]. In [56], the RPM case-history for the gas turbine exist as approximate GMMs in a plot of machine Shape and Directivity Index (SDI) vs RPM. In [57], it is shown that such rough and approximate GMM shaped data can be represented as smooth GMM shaped data using its mean value and covariances. In this paper, although the machine SDI vs RPM case-history are obtained from [56] it should be noted that such parameters can also be learned in the IIoT cloud using gas turbine data that has been generated at the IIoT system edge. The 320 MW gas turbine data RPM values exist from running speed of 1000 RPM to 3000 RPM. Although coastdown values can exist below 1000 RPM, coast-down are not considered since it can only exist when the machine is being turned off. To cater to the incidences of high synchronous speed [58] and to prevent incidences of spurious fault alarms, the gas turbine RPM values are extended to 4000 RPM with a peak SDI index of 0.8. To use the C28x DSP as an osmotic microservice device to generate the GMMs for the SDI/RPM data for the 320 MW gas turbine, the C28x DSP digital to analog converter (DAC) amplitude in CCS is set to 3.3E4. The reason for this DAC value is to obtain a GMM peak SDI value of 0.8 as shown in [56] since the range of the 32-bit digital to analog converter

Fig. 9. 2nd derivative of the 2-GMM showing 4 zero crossings

Fig. 11. 2nd derivative of the 3-GMM showing 6 zero crossings

ଶ̰ ଵ଺

(DAC) for the C28x DSP [24], [48] is ሺ ଶ ሻȀʹ= 32, 768. The 0.8 peak SDI value hence could be obtained for the needed GMM plots in CCS since for the C28x DSP, the DAC analog voltage waveform [24], [48] is given is

that the fog layer device has more computing power [52] than the IIoT edge device, hence a software application that usually needs more computing power, i.e., Matlab is used at this layer for cybersecurity applications. In this paper, cybersecurity applications for industrial high-power gas turbines are considered. Gas turbines is selected due to its application and versatility in several machines and industries such as its uses in aircraft engines (shown in Fig. 12) and in SG combined heat and power (CHP) generation. Gas turbines are also popular since they are available for low-power (8-9 MW, 13-15 MW, 48-75 MW, etc.) industrial use for example in Siemens SGT800, SGT-100, [53] etc. Typical low-power gas turbines application includes industrial mechanical drive applications, marine applications (such as hovercrafts and ferries), and in Auxiliary Power Units (APUs) for aircrafts [54]. Gas turbines are also available for very high horsepower applications examples of which include [55] General Electric’s (GE) SGT5-4000F (329 MW), and SGT5-9000HL (576 MW). To repurpose the C28x DSP as microservice provider supplying Embedded C based GMMs from edge to the IIoT fog layer for fault monitoring and IIoT cybersecurity applications, rotationper-minute (RPM) results of the case-history of a 320 MW gas

Voltageanalogue = Vref (

ீெெௐ௔௩௘௙௢௥௠஺௠௣௟௜௧௨ௗ௘ ோ௔௡௚௘௢௙ଵ଺ି௕௜௧஽ௌ௉஽஺஼

)...................(12)

In (12), the Vref is the C28x reference voltage, which according to [48] can vary from 0.0 V to 3.3 V. Thus, to obtain a peak SDI value of 0.8 for the C28x based GMMs, a Vref value of 0.83 is selected for GMM construction using Embedded C in CCS. Thus, by using DAC amplitude 3.3E4 as shown in Fig. 13, resulting GMM voltage peak in DAC will be Voltageanalogue = 0.80 (

ଷଷ଴଴଴

) = 0.8056.

ଷଶǡ଻଺଼

To realize the GMM for the 320 MW gas turbine, sine wave clipping, sequencing and concatenation method (Fig. 2) is used to create the GMM for RPM value ranging from 1000 to 4000 RPM. Since the C28x DSP only accommodate sample values up to 521 [48], the GMM RPM values are normalized by a factor of 20 and the resulting GMM is shown in Fig. 13. The

332

GMM overlap priors are set at 0.3 to prevent excessive overlap between the reference RPM value indicated by the first Gaussian marginal and the second RPM Gaussian marginal which indicate gas turbine RPM values tending towards a heavy rotor-to-stator rub. Any RPM rotation sample over the range of these marginals while the machine is running and under load will indicate a case of light rotor-to-stator rub fault for the first marginal, and a case of heavy rotor-to-stator rub fault for the second marginal [56]. To show usage of the constructed GMM as a C28x based microservice GMM supplied from edge to the IIoT fog layer, 170 samples of the normalized gas turbine RPM GMM samples are exported to Matlab using Excel .csv file format. Three different outlier detection rules, including Hampel Identifier, 3-Sigma rule and Boxplot method are considered for use at the IIoT fog layer for both machine fault monitoring and cybersecurity applications. As shown in [59], each of the rules have their strengths and weaknesses in detecting outliers in data samples. In [59], it is shown that the Hampel identifier uses more stringent criteria in detecting data outliers since its upper and lower outlier threshold is closer to μേ 2ߪ when compared to Boxplot method. The Boxplot method is also shown to be able to detect more outliers than the 3-Sigma rule. Hence according to [59], the outlier detection precision of each rule relative to each other could be represented as

The Boxplot rule could be represented as ‫ݔ‬௜ ൐Q3 + 1.5 IQR ‫ݔ ڂ‬௜ ൏ Q1 െ 1.5 IQR ..............................(17) where IQR = Q3 െQ1 in (17) is the interquartile range. Q1 is the upper 25th percentile. The sample median Q2 or ‫ݔ‬ොis the middle 50th percentile, while Q3 is the upper 75th percentile To improve on computing speed at the fog layer while at the same time monitoring the IIoT system for both cybersecurity threats and for machine faults, the Hampel identifier due to its superior outlier detection property is deployed for cybersecurity protection while both Boxplot and 3-Sigma rules are deployed and compared for machine fault monitoring. For osmotic collaborative computing, the C28x Embedded C based GMMs from the edge are shared with the fog layer device, a PC in our case, and Matlab is used to evaluate data from the edge machine for both cybersecurity threats and machine faults. Excel .csv samples of GMM from the IIoT edge C28x DSP are scaled down by a factor of 32,768 (i.e., 32-bit DAC range) at the fog layer Matlab to maintain an 0.8 peak SDI index. Hampel identifier rule is used to protect the edgeconstructed GMM that have been collaboratively shared with the fog layer device, and the protected GMM is stored in the fog layer device (PC). Upper and lower MAD bound of the Hampel identifier for the GMM cybersecurity protection are shown in Fig. 16. The same GMM with more stringent Hampel identifier MAD that is slightly lower than the μേ 2ߪ –Š”‡•Š‘Ž†—•‡†ˆ‘”–Š‡ ‹‰ǤͳͶ  is shown in Fig. 15.

Hampel • Boxplot • 3-Sigma rule ...................................(13) The 3-Sigma rule could be [59] represented as | ‫ݔ‬௜ െ  Ɋො | ൐3ߪො....................................................................(14) where Ɋොand ߪො in (14) are the sample mean and sample standard deviation respectively [59]. The Hampel identifier could be represented as | ‫ݔ‬௜ െ  ‫ݔ‬ො | ൐ĮS.....................................................................(15) where ‫ݔ‬ො in (15) is the sample median and S, the median absolute deviation (MAD) scale estimator could be represented as S=

ଵ ଴Ǥ଺଻ସହ

median {| ‫ݔ‬௜ െ  ‫ݔ‬ො |} .............................................(16)

Fig. 14. Hampel identifier used on the Embedded C based machine GMM at the IIoT fog layer to detect cybersecurity threat

Fig. 13. GMM constructed for the C28x DSP using Embedded C in CCS for the 320 MW gas turbine rotor-to-stator rub cases [56]. Any sample values above the GMM will indicate machine faults of (1) light rotor-to-stator rub, (2) heavy rotor-to-stator rub

Fig. 16. Hampel identifier cybersecurity or serious machine fault detection

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Fig. 15. Hampel identifier with improved MAD to detect cybersecurity threat at IIoT fog layer

Fig. 17. 2D-GMM and 1D-GMM comparison of the gas turbine RPM data

Fig. 20. 3-Sigma rule for machine fault detection (machine light rotor rub)

Fig. 18. Boxplot rule for machine Fig. 19. Boxplot rule for machine fault detection (heavy rotor rub) fault detection (light rotor rub)

Fig. 21. 3-Sigma rule for machine fault detection (machine heavy rotor rub)

cybersecurity attacks and for IIoT machine fault monitoring. Our contribution in this paper is the first known use of the C28x DSP as a GMM generator. IIoT machine parameters (mean and covariance) can be learned in the cloud, using machine generated data and the learned parameters can be used at the edge by low-cost C28x based devices to construct GMMs that can be used in novelty and outliers’ detection, which are important machine learning activities. Different programming languages such as Embedded C (at the IIoT edge layer by the C28x DSP) and Matlab (at the fog layer by a PC) are used to show how software defined osmotic computing can be used to allow both low and high-computing power devices to collaboratively participate in IIoT computing at different layers of the IIoT network. Uses of different rules including Hampel identifier, Boxplot and 3-Sigma rules are shown for cybersecurity and outlier detection application for the case of a 320 MW industrial gas turbine. Further work in this area will include use of the widely available, low-cost C28x DSP for other machine learning applications for IIoT systems.

These Hampel identifier based GMM machine RPM data samples can be shared collaboratively shared among several edge and fog layer devices and stored as the reference machine RPM reference data. Any small samples [59] of new GMM representing a windowed machine RPM data generated at any time by the rotating machine can then be compared with the Hampel based reference GMM such that incidence of spurious/untrue machine data set representing cybersecurity threat can be detected at the fog layer. Thus, cybersecurity attack can be detected, and if possible prevented by an alarm signal sent to both the edge and IIoT fog layer (Fig. 1). A possible use of the Hampel based GMM for cybersecurity threat detection is shown in Fig. 16, where the threshold of new machine RPM data set possibly supplied by a hostile attacker is detected at the fog layer. Fig. 17 is a 2D-GMM representation of the machine RPM data, with their associated 1D-GMM marginals for the for the case of light rotor rub (x-axis), and heavy machine rotor rub (y-axis), also shown. For fault monitoring, both Boxplot and the 3-Sigma rules are used on the 2D-GMM and compared. RPM data under the Embedded C based GMM threshold is randomly generated, and outliers in the data sets are detected. It is observed that for the case of light rotor rub machine fault, both the Boxplot (Fig. 18) and the 3-Sigma rule (Fig. 20) detected three RPM outliers (shown in black rings) at RPM thresholds lower than the 1000 RPM value. Also, both the Boxplot and the 3-Sigma rules detected five RPM outliers (shown in green rings) in the case of extremely high machine RPM than the 4000 RPM threshold as shown in Fig. 19 and Fig. 21. This indicate a case of heavy rotor rob fault. This approach signifies that both Boxplot and 3-Sigma rule can be deployed together at the fog layer, and relevant alarms can be shared with the edge and cloud in cases of machine faults.

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