GAP in Multichannel IoT data analysis
In my recent article, “Usher Syndrome in IoT — and a Cure” (June, 2021; https://pgmad.medium.com/usher-syndrome-in-iot-and-a-cure-4c32cf6ffd0a), I discussed the current gap in IoT data analysis where each channel is treated on its own individually — the “looking through straws” problem! Multiple channels of data that flow into an IoT platform need to be treated TOGETHER (within and across channel) to be able to extract maximum information from our expensive IoT installations.
Multi-channel IoT time series can be treated as a vector time series. Vector time series at each sampling instant are correlated in time to past samples; if we think of each channel as a “node” in a causal graph, we can call the causal factors among them as “self-node” and “inter-node” lagged causal factors. In addition, if you take a snapshot at one time instant, there will be relationships among the elements of the vector time series which leads to “inter-node” structural causal factors — there is no time element here — hence “structural”; it is an instantaneous picture. It turns out that STRUCTURAL causal factors are super-important (which we do not consider in IoT at all); they are KEY to filling in the picture between the individual channels!
Causality in IoT is different from causality in, say, Social Sciences or Health Sciences. There are NO self-structural causal factors, i.e., a node cannot be a cause of itself — seems reasonable. But in those fields, circular causality between two or multiple nodes are also verboten! In my slide presentation, “Multichannel IoT Causal (MIC) digital twin” at https://www.slideshare.net/PoovanpilliMadhavan/multichannel-iot-causal-digital-twin, on Slide #13, I show why this restriction should not apply to engineered systems like IoT (because of ADC sample-and-hold duration). So, while causality in Social Sciences leads to Directed Acyclic Graphs (DAGs), causality in IoT should lead to Directed Cyclic Graphs (DCGs) with no self-cycles in both cases.
Assuming we have Lagged and Structural causal factors estimated from multichannel sensor data in hand (see “Causal Digital Twin from Multi-channel IoT “, June 2021; https://arxiv.org/abs/2106.02135 for full technical details of estimation), visualizing them is a major challenge due to a variety are factors that I discuss below.
Usual graphs do not suffice since we have to show causal factors among current and past data points. Ladder diagrams where each vertical “post” is a time instant is a possibility; the only reference you will find for Ladder Graphs is Wolfram MathWorld where ladders with only horizontal rungs are discussed. It turns out that for our work in analyzing multichannel IoT causality holistically, we need more than that. This will become clearer when we explore an example.
Figure 1. Example Ladder Causal Graph
There are 4 horizontal “step supports” shown as B1, B2, B3 and B4 (with T or T-1 appended) which are the channels of IoT data from, say, 4 different sensors measured simultaneously. The middle and right “posts” show the channels at the CURRENT (same) instant of time, “T”. The left “post” is for the just-past instant of time, “T-1”. GREEN indicates a Lagged causal factor when it exists and BLUE indicates a Structural causal factor if it is non-zero between two channels. Solid lines indicate a positive causal effect (cause will INCREASE the effect) and a Dashed line indicates a negative causal effect (cause will DECREASE the effect). The thickness of the links is proportional to the magnitude of the links (causal factor magnitude) between the nodes.
Walking through figure 1, we see a Lagged causal effect between B1:T-1 at the top left and B2:T in the middle. In words, B1 from the last instant will cause B2 to increase (solid line) at the present time. For another example, B4 at the present time will decrease B2 at the present time — I am sure you see the picture (B4:T and B2:T are connected by a BLUE dotted line). There are NO horizontal rungs on the right-hand side since Self-Causality are not allowed per discussion earlier.
The 4 horizontal rungs on the left-hand side is an expected phenomenon: they are the Autoregressive model (order =1) coefficients; these “AR(1) coefficients” are the Lagged WITHIN-channel causal factors; they will be non-zero as long as time series is auto-correlated which will almost always be the case with IoT data.
If we update the Ladder Graph at every instant of time (usually not necessary in IoT applications!), a new set of causal factors will “enter” from the right as the middle post “rolls” to the left, i.e., Current data of last instant becomes the Last data of the current instant. Last data of the last instant “falls off” the left-hand side. This dynamic suggests a rolling cylinder with causal factors plotted on its curved surface with the cylinder rolling from right to left. Such a visualization is yet to be created . . .
With the basics of Ladder Graph out of the way, we can delve deeper into graph analysis. Traversing the paths from left to right will reveal many key dynamics of the system measured by IoT. They contain information of the current performance and what may happen in the future. From such a description, we can perform “what-if” analysis and “counterfactual” experiments to see the possibilities of the underlying system, be it a machine, a set of interconnected machines, a plant, a building, a city, . . .
Here is a simple example. In figure 2, we show the lagged and structural causal factors in a bearing system test (4 bearings as shown on the left), one day before (D-day -1) bearing, B1, failed.
Figure 2. Ladder causal graph of a 4-bearing system
To make the hitherto-unavailable multichannel insights visible, I have overlayed the RED arrows showing how Bearing, B1, becomes the end effect of many causes that increase its vibration energy. The red isosceles triangle (inverted) at the top is very problematic — it is a positive feedback loop with “runaway” destructive possibilities! No wonder B1 failed the next day!
In fact, isosceles triangles are interesting geometric objects in Ladder graphs. They can be inverted or right-side up. If all the links are positive (solid lines), it portents a runaway situation leading to or already in an Unstable condition. We can tabulate the possibilities as follows:
I believe that there are more “geometric objects” to be discovered in Ladder graphs that may lead to more insights; programmatic analyses can automate such a system for insight generation.
The other RED arrows are also meaningful; for another example, B2 feeds energy from (T-1) — past instant — to B2 at the current instant (T) which instantaneously feeds part of that energy to B1. The interplay between past and present instants and between different bearings are very revealing indeed — it is likely that an automated graph analysis software will reveal more paths than what I have identified in figure 2.
Even more importantly, a machine dynamics expert can take look at this and immediately see how the bearing spacing, shaft stiffness, damping, etc., should be altered so that such a failure will not happen again. Additionally, the changes planned can be explored by adjusting the causal factors on the Ladder graph to see exactly how the vibration amplitudes and frequencies change — NOTE that such an analysis is reliable ONLY if you have the causal picture and not a “correlation” picture.
All the technical and application details are available in my slide presentation, “Multichannel IoT Causal (MIC) digital twin” at https://www.slideshare.net/PoovanpilliMadhavan/multichannel-iot-causal-digital-twin and related publications listed in the presentation.
Applications are many. Wherever there is IoT data as multi-channel time series, our Causal Digital Twin can be applied for causal discovery and causal estimation to achieve significant operational objectives as the examples below show.
Consider the following IoT use cases that generate multi-channel time series:
1. A manufacturing plant production line with a set of machines with connected sensors; objective: Increase Production
2. A building with monitoring data from HVAC system, occupancy, lights and computer operation, water usage; objective: Minimize energy usage
3. A retail store that monitors shelf facings, back-room store, shopper density, POS terminal data; objective: Reduce OOS (out-of-stock) problem
4. A smart city operation where multiple feeder road traffic and major intersections are monitored in real-time; objective: Real-time traffic engineering to minimize congestion at the intersection
IoT technology is now ready to go beyond “looking through straws” and extract the FULL picture to help our clients improve productivity and quality as well as reduce waste, thus increasing gross margins.
Dr. PG Madhavan
