Expendable and Distributed Measurement Scheme for Acquisition of Naturally Sparse Events

A common reason for electronic measurement anomaly is the inadvertent rise in ground potential with respect to measurement ground. The ground potential rise happens during current leakage to ground from lightning or from power grid and leads to catastrophic failure unless appropriate preventive action is taken to isolate the sensitive measurement systems. A networked system for acquisition and transmission of ground potential measurements to data monitoring station is presented here. The system is aimed to implement using low-cost IoT devices with limited resources since these units are planned to be expendable. The limited processing power of such devices is not sufficient to run high efficient computation intensive routing algorithms. A lightweight routing algorithm for this purpose is proposed here. The discussion on reliability of such systems is also presented. The multipath route discovery strategy presented here reconfigures the network to an optimal configuration with respect to energy dissipation and node distribution.


Introduction
Events with naturally sparse measurement signature are lightning induced ground potential rise, earthquake or tsunami triggered seismic events, hurricane and flood triggered water saturation and land slides, solar flare induced electric and magnetic field variations. These events are rare and result in extreme inconveniences. However there are large number of widely distributed binary sensor systems for detecting such extreme events, in many case these warning systems are signal threshold based detection and the measurement are detected when it is large and some times the damage starts when the events are occurring. All of these events generates typical precursor signals, however these signals are oftern 1 3 missed due the lower acquisition rate, not due to the low sampling rate as extremely fast signal sampling systems are available for measurement and storage of all of signals. The event missing depends on how the sampled data is acquired and this needs no explanation that these rare events are not possible to measure and acquire from the data analysis lab. The sensors need to be widely distributed in event prone remote locations. It it easy to establish high sampling rate system in every location to capture the typical precursor signals, however bringing these signals to the labs for real time analysis is important. The solution to this problem is simple, use high bandwidth communication systems. But it is not cost effective and impractical. An alternative solution is to use compress the data and transmit through low bandwidth communication framework. But there exist a method of measuring and compressing at the same time and it is widely studied and used in various applications like synthetic aperture radar signal measurements and MRI. One way to increase the chance of detection is to spawn expendable low cost measurement systems widely and establish a communication network for acquiring these signals. The Internet of things based measurement system provides the low cost expendable measurement and processing platform and here we discuss about the networking that can be implemented using these units for acquiring the measured signal using the concept of wireless sensor networking systems. There exist advanced systems and algorithms for all the processes that are explored in the paper, what is being discussed is how to optimize system to a minimum level so that it is implementable using expendable IoT platforms. This contents of this paper is organized into three sections the measurement of sparse events, distributed acquisition and reliability.
The accurate measurement of ground potential voltage at distributed locations inside a plant is necessary for correcting the offset in the corresponding ground referenced measurements for better data interpretation; especially in industrial process control applications. This offset is transient and exist only for a short duration < 200 μs and in most of the time the value is zero. The sampling rate has to be high to capture these transient characteristics in the signal. Considering the large number of such distributed measurements the data generated will also be enormous. Four problems need to be addressed in this scenario namely the measurement of transient signal, handling of large amount of data, the transmission of the acquired signal to the data processing station and finally the implementation of the system. Considering the implementation of the system, it needs to be low cost and expendable, because, even if high reliable components are used in the fabrication of these devices, the degradation is eminent as long as they are left outside. Hence the low cost IoT based devices are selected in such scenario. But, such devices have processing capabilities limitation that constrains the implementation of data acquisition, data handling and the communication processes. The sparse measurement method is adopted here to solve the first two problems as described in Sect. 2. Also the processing requirement is relatively low compared to conventional high speed data acquisition and compression process, as the sparse measurement combines the data acquisition and compression into a simpler process of matrix multiplication. This gives triple advantage of high speed acquisition, data compression and simplified computation. Also, the processing can be done in the limited resources of IoT devices. Considering the transmission of measured data to data processing station, the use of copper cables is infeasible as the communication cables become electrically polarized during lightning and causes damage to the devices interfaced to it. In such case the measurement system will be the first one to fail. However, wireless sensor network can be used in this scenario as these are independent, easily deployable and scalable and implementable using IoT devices [1,2]. A trivial solution is to implement a data collection node with multiple data acquisition and transmission nodes. But this is 1 3 limited by the communication range of the underlying physical layer. To spread-out the data acquisition units in a wider area a routing mechanism need to be implemented for data acquisition and transmission nodes; and at the same time implementable using IoT devices with limited capabilities. Some of the algorithms available for such routing are Dijikstra's algorithm (DA), ad hoc on demand distance vector routing (AODV) [3], ad hoc on demand multipath distance vector routing (AOMDV) [4], secure multipath load balancing-AODV [5]. The low energy adaptive clustering hierarchy (LEACH) [6] with self-organization and adaptive clustering feature is the base of many of the power aware routing algorithms. The algorithm is compared with other power aware routing algorithms like Energy efficient clustering (DEEC) [7], Immune cooperative particle swarm optimization (ICPSO) [8], Extended stable election protocol (ESEP) [9] and Energy-efficient, delay-aware and lifetime-balancing data collection protocol (EDAL) [10]. Other energy conservation options in WSN are spectrum sensing and channel allocation [11] and Efficient energy-aware routing with redundancy elimination [12], but in these the route configuration is fixed and not randomly deployable. The implementations of these algorithms demand high computational power as these algorithms are designed for high efficiency routing applications; but, if the implementation platform is a low cost IoT processor the cost of computation is a major factor. A comparison of these algorithms is given in Table 1. A similar work on combining compressed sensing and MAC protocol design is presented in [13]. A custom protocol development scheme for adaptive multipath load balancing scheme based on disjoint links found from path vacant ratio is given in [5]. A node distribution strategy maximizing the coverage is described in [14]. A survey of multipath routing protocols and its classifications is given in the paper [15]. A comparison and evaluation-metric for multipath routing algorithms can be seen in [16] and a survey of Bluetooth multi-hop networks including low energy mesh networks is given in [17]. Power dissipation can be further reduced using radio duty cycling protocol [18] or straight line routing protocol [19]; but these are not considered as they need platform hardware change. The geographical energy aware routing is not considered as this requires GPS based triangulation method for route discovery. Based on various wireless sensor network schemes studied in [20] it is observed that IEEE 802.11 based solutions are suitable in such applications. A general guideline for design Table 1 Parameter usage, cost function and complexity of routing Algorithms d-hop distance, T-propagation delay, L-link speed, E r -residual energy, P-Tx power or bandwidth, W-link weight. n-number of nodes, r-number of routes, f()-some function, c ij , x ijk -algorithm specific parameters, Ω k -cluster set. dv-distance vector, acc-accumulation, heur-heuristic, Tgrph-Topology graph, PD-packet delivery, T -throughput. ACop-Ant colony optimisation, PSO-particle swam optimisation Route. Complexity Cost function and analysis of sensing network can be found in [21] and a frame work for MAC protocol modeling is given in [22]. The reliability of the network is estimated using accelerated testing concept described in [23]. An empirical expression for reliability estimate using Eyring model is described in [24]. The quantitative estimation of the reliability of the proposed network is given in Sects. 3.6 and 3.7. The conclusion is given in Sect. 4.

Ground Potential Measurement
The lighting flash from 1 to 10 km altitude cumulonimbus clouds span for 50-200 ms with a discharge peak near 10 μs . The ground potential rise due to lightning current leakage to ground is expressed as V r = I 2 r , where is the local surface resistivity of earth in Ωm , I is the leakage current, r is the radial distance from the lighting strike point [25]. The Fig. 1a shows the peak time value of the simulated potential during electrical discharge. The lightning induced ground potential is simulated using matlab model 1 and the transients are acquired using simulink model. The simulink schematic is similar to one used in [26] for wide band signal acquisition for spectral estimation. The transient nature of this signal can be observed from Fig. 2a. In ground potential measurement the reference ground is infeasible hence two electrical probes at a distance apart measure the relative potential difference. The probes located in radial direction measure large potential difference compared to electrodes along the tangent to the equi-potential field as shown in the Fig. 1b. The Schlumberger resistance technique is used to calibrate the measurement device. The differential potential developed can be written as (1) where d is the spacing between electrodes. Ground Potential Rise (V) Fig. 1 a Simulated ground potential using 3.2 A 10 ms DC discharge pulse causes proximately 5 V ground potential rise along 5 m radius in wet Clayey sand with 50 Ωm resistivity. b The contour of ground potential rises. The voltage sensed by the isolated differential probes [A, B] in the radial direction to the field is high compared to the measurement by the probes [C, D] in the tangential direction to the field As this transient voltage exist only for a short duration < 200 μs ; based on sampling theorem this signal should be acquired least at 5 KHz. Due to sparse nature of the event most of the time the measurement is zero. However to get the transient characteristics the sampling rate cannot be compromised. Considering the large number of such distributed measurement units the data generated will be enormous. 1000 such measurement nodes will generate 5000 K samples per second, that needs a bandwidth of ≥ 50 Mbps at data collection node. This data requirement is more than the specifications of IoT devices. As discussed earlier the compressed sensing technique can combine the data acquisition and compression into a simpler process of matrix multiplication and can be done in any low profile computational units, hence the sparse measurement method is adopted here to reduce the sampling rate.

Ground Potential Acquisition using Sparse Measurement
Compressed Sensing is a signal measurement and compression technique for sparse signals, where the analog to digital conversion can be done at sufficiently smaller sampling frequency compared to the Nyquist sampling rate [27]. For any arbitrary signal x ∈ ℝ N with K-sparse representation z ∈ ℝ N (‖z‖ 0 = K) in some basis B and with x → z transformation given by x = B z, (B ∈ ℝ N×N ) the theory states that the signal x can be measured as y with M ≪ N samples from a linear sparse-projection space B using a measurement matrix A.
where B −1 ∈ ℝ N×N is the transformation matrix to convert x to sparse z . If the signal to be acquired x is sparse, ‖x‖ 0 = K ≪ N then = . The recovery of K-sparse signal from M measurements is possible when the following preconditions are satisfied. (cond. i) The null space of measurement matrix A do not contain any 2K-sparse signals (3) [28]. (cond. iii) The columns of the measurement matrix A are independent and iden- [28]. (cond. iv) The maximum variation in L 2 norm of the measured signal = −1 x relative to the original signal should be bound by the limit 0 < | K | ≪ 1 defined as restricted isometric constant (5) [30].
The conditions given in (5) is necessary and sufficient and when satisfied the other conditions are implicitly satisfied. However, the condition (5) is hard to verify prior to the measurement of y , as the signal x comes in contact with the measurement system during the acquisition only. The theory described in [31] gives solution to this problem.
(cond. v) The minimum number of samples (M) to have the recovery probability of 1 − is given in (6), where C > 0 and ≤ K . The graph of this relation is given in Fig. 2c.
As the transient signal acquired is in compressed form, it needs to be reverted back to its original form prior to use. The voltage profile is reconstructed from the measurement using L 0 minimization given in (7) with small error ≈ 0.
This optimization involves large computation, however this processing is not meant to be done in IoT process and it is not a concern. There are many variation of the algorithms for this purpose, but not discussed here as this is not concerned with respect to the scope of this paper. But for completeness of discussion some recovery algorithms are mentioned. The sparse signal vector z has two distinct features, the non-zero value's support location supp(z) = {i ∶ z i ≠ 0} and the magnitude of non-zero values at these locations. There are two main class of recovery algorithms, the greedy matrix minimization and the function minimization to estimate the sparse signal z . The L 0 minimization is nondeterministic in polynomial time (NP) hard problem in terms of function computation because of the combinatorial search required, it is very large even for smaller vectors. However, modified L 0 function approximation methods like xL 0 − eL 0 (XEL0) [32] or radial basis function based sparse recovery [33] does some alternate ways to minimize the computation requirement.
The computation in XEL0 algorithm is summarized as minimize ‖z‖ 0 and ‖e‖ 0 by iteration using polynomial approximation subject to the recovery error e = A † (y − Az) < and scale down the function gradient in every iteration with smaller scale factor k = 0 k . The RASR algorithm minimizes ‖z‖ 0 and least square error alternatively using two cascaded network and the initial value used in both case is z(0) = † . The voltage transients recovered using these methods are shown in Fig. 2b. In general any of the sparse recovery algorithms can be used for this purpose.

Wireless Sensor Network
Having acquired the data it needs to be transmitted to the monitoring station. The network considered here consists of 3 types of nodes, the nodes with direct interface to data processing station (N0 nodes), the nodes with data routing and data acquisition functions (APQ nodes) and the nodes with data acquisition and transmission functions (AQ nodes). The strength of the network depends on the effectiveness of the logic build into its routing algorithm. Routing algorithms in general use clustering or forwarding schemes, clustering is computationally demanding and is suitable for high speed low data frame size networks. The frame forwarding scheme is optimal for low data rate networks. A simpler protocol is needed for low profile IoT boards. The table I shows the computational complexity of some of the currently available algorithms. Here we try to develop a light-weight routing algorithm. Four factors are considered as most essential; namely energy efficiency, data communication reliability, data security and its maintainability. While considering reliability as primary concern the multipath routing is optimal since it reduces the system unavailability due to node failures. Considering the data synchronization issues of multipath routing, the stand-by redundant multipath routing technique is effective. Here every node maintains a list of priority routes selected based on link cost estimation. These links will be used in later time if a failure is observed in the active link. The parameters used in the algorithm design are: number of nodes in the upstream path up to N0 node d GI , link speed L, bandwidth BW, battery energy level b / residual energy E r , received signal power P S and the data frame size F. The table I shows the parameter usage of some of the currently available algorithms.
The proposed routing strategy considers the above mentioned resources as constrained while determining the optimal route [34]. The network graph referred here is shown in Fig. 3. The algorithm first identifies its neighbouring access point nodes (APQ) or N0 node which satisfies the network discovery process described as where ℕ k the enumeration index of all possible neighbouring APQs, Ω k is the set of nodes such that the password Pwd can be decoded from the service set identifier (SSID). To identify all nodes as part of this WSN, the SSID is given the format 6 where each field is of the specified bytes long and SYS: system identifier, SEN: sensor type, YY SS: year and month of installation and NUM: sensor number, like [MET1611DFV000822]. After boot up the nodes scan all the WiFi channels for the compliance of the connection format and determines neighbouring APQs [35]. The node N k then generates the parameter matrix W k from the information available in the beacon frame of the observable adjacent nodes i … j ∈ Ω k .
where (i) indicates the node N i , d GI (i) ∈ (1, N max ) the hop distance, N max is the maximum links to reach the data processing node, P S (i) is the observed signal strength of the node N i , P min ≤ P S (i) ≤ P max ≤ 0 , P min , P max are the minimum and maximum transmission power and 0 < b(i) ≤ 1 is the energy reserve. The operator |.| 0 finds the number elements in the set and is the total number of neighbourhood nodes of N k . These parameters are used in the weight computation as exponential functions for accommodating wider range. The upper limit of bandwidth L(i) is accommodated using saturating function (1 − e − L(i) ) . The frame size F(i) include the node's own data frame size and frame size of other nodes for whichN i functions as router. A trivial routing from node N k to N i ( R(k) ) is to define a vector weight function w(ℝ 6× → ℝ ) and select a node with largest link weight (11).
where ( ), ( ), ( ), ( ) and ( ) are function normalization constants quantified in later section. The computation is further reduced by taking the inter dependency of the parameters. If the nodes generate same amount of data the cumulative frame size F(i) increases as distance d GI (i) to N 0 node reduces ( F(i) ∝ 1∕d GI (i) ). Hence these factors can be combined together. Similarly the maximum possible link speed depends on the carrier power as L (k→i) = B W log(1 + P S (i) P N ) , where P N is the ambient noise power [36]. Considering these dependencies the link weight function is simplified as (12) after setting 0 = B W . The transmitted signal power P T (i) of the node N i attenuates to P S (i) when it reaches the node N k and this is related as P S (i) = G T P T (i) 1 where G T and G R are the transmitter and receiver antenna gain, W is the wavelength and r is the distance between nodes. If all nodes transmit the beacon frame at P T (i) = P max power; and if the antenna gain is same (G A ) for all nodes the power ratio = 10 log(P T (i)∕P S (i)) can be written as (13).
If the node N k detects that the signal strength of the beacon frame P S (i) > P sen (sensitivity of the node), then decreases the link power to a minimum enough to meet the node N i 's sensitivity. From the relation G A P Tmin 1 4 |r| 2 2 W 4 G A = P sen the minimum transmission power required is given in (14).
The access point mode beacon broadcast from N k is maintained at P max . The data frame size is automatically reduced using compression feature of sparse measurement described in the previous section. This is also included in link weight function as increase in energy level parameter: b(i) = b i + c(i) , where 0 < c(i) < 1 represents the compression rate. The link weight function is changed as (15) after setting = .
This function can be implemented as 4 lookup tables corresponding to each variable. The network routing starts from the node proximal to N0 node. The APQ nodes connected to the N0 node, broadcast the beacon frame with the information { d GI (0) = 0 , L(0) = L 0 , F(0) = F 0 , b(0) = 1 }. If the node N k gets the beacon broadcast from multiple nodes like Ni, Nj etc, the routing algorithm R(.) determines the optimal node using (15) and establishes the connection.

State Parameters
After establishing the upstream connection, the node then defines its current state S k (16) using the available information, where Ch(k) is the WiFi channel, T pdi is the propagation delay and L(k) is the (N k → N i ) link speed of the upstream link. P S (k) is the received power and R(k) is the route table from the node to N 0 node.
The following parameters are updated with the information obtained from the upstream node: d GI (k) = d GI (i) + 1 , F(k) = F(i) + F k0 . where F k0 is its own data frame size and b(k) = b k . These values determine the quality of link through this node. The node N k then starts the transmission of its beacon frame containing state parameters in access point mode through its selected channel. The state parameters S k is also send to its upstream node. When the other downstream node N m connects to N k the frame size is updated as F(k) = F(i) + F k0 + F m0 . As new node connects to N m the frame size of N k gets updated again as F(k) = F(i) + F k0 + F(m) . This new information is updated through the beacon frame. Other nodes connected to N k can switch to any alternate node if the link becomes suboptimal for it. This adaptability strengthens the network structure.

Weight Scaling Parameters
The values of sensitivity and scaling parameters in the link weight function (15) are selected to keep w(W k i ) < 4 as given in (17) Using these values the link weight function is modified as (18). The graphical representation of this normalized weight is shown in Fig. 4. It is interesting to note that the node proximal to the data processing unit is not always energy efficient when the entire WSN is considered as a single entity.

Failure Detection and Routing Switching
The data unavailability due to intermediate node failure is avoided by switching to alternate link when no-response is obtained within T pd time. To determine new link the route logic is modified to N-point routing algorithm R N (k) this gives a set of indexes V k ⊂ Ω k ordered according to its weight.
where |V k | 0 = N < |Ω k | 0 = . The algorithm selects M links for multipath routing. The route table information (20) for data routing from an AQ node at the boundary of the network ( N b ) to data collection node N 0 ( N b → {N k } K → N 0 ) is collectively obtained from the route table available in the state parameters S k of the upstream nodes.
where Ω = ⋃ K−1 k=0 Ω k . The route table R(b) is included in the system parameter S k to avoid cyclic routing and if the node finds its own number that path is avoided. Based on the routing strategy discussion above the resource constrained adaptive multipath routing (RCAMR) for autonomous sensor network is described in Algorithm I. The timing diagram of the communication protocol is given in Fig. 5.

Network Analysis
According to the communication scheme discussed the access point node control the data transmission. The protocol timing of communication between upstream node N 0 and downstream node N 1 is illustrated in Fig. 5 with respect to the N 1 node. The node senses the upstream communication link for t sense duration and if the channel is available, transmits its load of data to the upstream nod. This communication exists for t tx duration. Upon successful communication the acknowledgment frame is received from the upstream node and the channel is left in sense mode. Other nodes for which N 0 is upstream, transmits their data. The entire upstream communication extends up to t tx cycle duration depending on the number of nodes connected to N 0 node. When all nodes have transmitted data the N 0 node broadcasts the beacon frame containing the state parameter information S 0 for t bcx duration. All the nodes are programmed to remain in idle mode for t idle duration after the beacon frame reception, during this time the network is available for other nodes waiting to establish connection. The upstream communication cycle continues after this idle time. In the downstream the communication happens in a different channel Ch2. The N 1 node in access point mode listens to transmission from its downstream nodes. The data is received in succession from its n downstream nodes. For every successful reception the N 1 node transmits ack frame. This communication lasts for t rx cycle . After reception, the node senses the channel for t sense duration to confirm the channel silence and the node then transmits the beacon frame containing its state parameter S 1 . As earlier, all nodes in the network remains in idle mode for t idle duration and during this time the network is available for other nodes waiting to establish communication with N 1 . The following definitions are made to have a clear understanding of the communication protocol. The data aggregation network established by the node N k is synonymously called as network N k , Ω k : set of upstream nodes of N k , Φ k : set of downstream nodes for which N k is the access point, P(N l ) transmission probability of node N l in the network N k , P(c k |N l ) conditional probability of collision when N l transmits. The probability of collision in the network N k can be written as P(c k ) = ∑ l∈Φ k P(c k �N l )P(N l ) . However, the conditional probability of collision is difficult to estimate for every node. The probability of any transmission in network N k can be expressed as (21) The probability of collision free transmission happening from any downstream node N m to N k can be written as When the node N k is working reliably, the probability of successful reception by N k is same as probability of successful transmission from all the nodes in downstream network as given in (22) Using these 2 expressions the collision probability can be expressed as P(c k ) = P(t k )(1 − P(r k )) . The probability that the network N k is in the idling state can be written as P(i k ) = ∏ l∈Φ k (1 − P(N l )) = 1 − P(t k ). If t c is the average collision time per cycle observed in the network, the total channel usage time for one communication cycle using the protocol can be written as where |.| 0 gives number of elements in the set. The effective time utilized by all the downstream nodes ( N l , l ∈ Φ k ) for real data communication including basic Headers (H), short interframe space ( S SIF ) and acknowledgment ( A k ) is computed as where L(k) is the link speed and T pd is the propagation delay of the network. F(m) is the frame size of the N m node. The throughput of the network N k can be computed as The state transition diagram of the protocol and the timing diagram of the communication protocol using the described algorithm are given in Fig. 6. The communication channels are colour coded as the network described in Fig. 3.

Power Dissipation
The factors that determine the practicality of WSN routing algorithms are energy dissipation, number of nodes retained and the distribution of nodes after certain amount of routing cycle. The power dissipation of the routing algorithm is computed using the following expressions (26).
The parameters are set as follows: initial energy E 0 = 1J , bit processing E el = 50nJ , data aggregation E da = 5nJ , RF amplifier system E amp = 100 pJ , frame size F(i) = 4000 and number of nodes N = 100 . The probability that the node function as cluster head is p = 0.5 . The algorithms used for comparison are LEACH [6], enhanced SEP [9], and DEEC [7]. The simulation is run till 50% of nodes get depleted of its energy. The Fig. 7 shows the energy consumption in the network established using various algorithms. The energy dissipation of the proposed algorithm varies during multipath route switching when the number of nodes start falling below 95%. After 50% of the nodes get depleted the power consumption in the algorithms varies considerably. With the same initial condition, number of active nodes falls to 50% in 600 to 1000 routing cycles for the algorithms compared while the proposed RCAMR algorithm takes 2.8 times longer for 50% power depletion. The node attrition rate of these clustering and routing algorithms is shown in Fig. 7b. It is observed that when the nodes use RCAMR algorithm there is considerable increase in the lifetime of nodes and hence the overall network. The advantage of the proposed algorithm can be seen when analysing the distribution of the nodes in the network after half of the nodes get depleted. The node distribution at 50% energy level is shown in Fig. 8. The . 6 Timing diagram of network communication RCAMR algorithm retains the overall node distribution of the network for longer duration, at the expense of finite increase in energy consumption. This signature can be seen in the energy graph Fig. 7b, while network using other algorithms are at the end of its lifetime the proposed algorithm reconfigures the network to remain active. This algorithm retains the network 1.5 times longer than extended stable election protocol. this is the consequence of progressive reconfiguration of the routes to minimize the energy consumption of the entire The overall distribution of the active nodes is maintained by RCAMR even after 50% of the nodes is depleted network Hence in network established by RCAMR the distribution of the measurement is maintained for longer duration and is suitable for applications where this distribution of the measurements are necessary.

Reliability of Multipath Routing
The reliability of the network with K routing nodes in series from the boundary node N b to the sink node N 0 (N b → {N k } K → N 0 ) can be computed as (27).
where R(b) is the route table described in (20), Ω is set of all nodes, Ω is boundary set, t is the operational duration, k = 1∕t Fk and t Fk is finite mean time to failure of the node N k . The fault tolerance is achieved using M links (V k i , i = 1 ⋯ M) selected by R N (k) for multipath routing. The reliability of this configuration is given in (28) assuming the measure of reliability e − k t is identical for all nodes.
Every node N k maintains N number of routes leading to the sink node N 0 connected through to the K − 1 links. Considering nodes with different reliability measures After sorting elements of Λ k in ascending order corresponding to nodes with higher to lower reliability, the set can be split into two parts (i) Λ m k with m elements (ii) Λm k with m = N − m elements. The reliability of this redundant routing network can be written as (29).

Reliability Estimation by Testing
The network reliability evaluation based on the measurements obtained from the accelerated degradation testing is presented here. The processes that affect the system reliability are (i) thermo-mechanical (TM) stress induced failure like PCB warping, track breaking or solder disconnection, (ii) electrical (EL) stress induced failures like electro migration or track burn out and (iii) thermo-environmental (TE) stress induced failures like dendrite formation on PCB. Considering these effects the reliability of the network can be estimated through accelerated degradation testing of a sample node. Using the Eyring model [24] the mean time to failure (mttf) can be written as (30).
where S is stress, T a is accelerated testing temperature, T 0 is the operational temperature, t F(.) is the estimated time to failure during accelerated testing, T is the power of temperature interaction, A i and B i are empirical constants determining the stress interaction, ΔS i and ΔS T i are the difference in stress and stress per temperature rise experienced in operational temperature and accelerated test temperature. k B is the Boltzmann constant and E is the activation energy of the PCB track metal. The time to failure due to thermo electrical stress induced electro migration is given in (31), where J 0 and J a are the current densities at the dendrite formation point at operational and accelerated testing temperatures.
Time to failure due to thermo environmental dendrite growth t F(TE) due to high humid environment is given in (32), where R H0 is the ambient relative humidity, V 0 the maximum electric field experienced between PCB tracks, and D 0 is the average distance between PCB tracks.
Using the estimated mttf the reliability computed in (28) and (29) is modified as (33) where The combinatorial term ( N m ) can be avoided using the Local Theorem of DeMoivre − Laplace , which defines the probability of m instances of N events as follows.
where p = e − k t is the probability of functioning of a unit, q = (1 − p) . and P N (m) is the probability that m instance of N units function correctly. Using (34) the reliability of the redundant routing network can be expressed as (35).
For a simple multipath network with 9 nodes, one source, one sink and 7 routing nodes with 2 out of 3 redundancy, the reliability expression is computed as (36) and is shown in Fig. 9.
The figure also shows the computed reliability value from DeMoivre-Laplace theorem and the value obtained from the binomial theorem; for estimation purpose the reliability can be computed using (35). It is observed from Fig. 9 that as the design constraint for the node becomes stringent (higher t F values), the reliability of the network increases. The reliability of the network during initial 7 year period of operation is > 0.75 . The low-cost IoT processor based devices can be used for parameter monitoring, if it is planned to be replaced in every 3 to 4 years, to have reasonably high confidence level on the WSN. Even if high reliable components are used in the fabrication of these devices, as long as these devices are left outside they will degrade. Hence it is logical to use low cost IoT processors based WSN devices with a plan for regular replacement or additions, also, considering the cost of the plant maintenance the cost involved in the short time usage of low cost IoT based devices for sensor network will be negligible.

System Evaluation
The features of IoT platform processor considered are the cost, availability of development environments, OS and file system support, programming modularity and availability. The WSN nodes with compression features are created using TI CC3200 WiFi processor based boards with transmitter power P max = 17.3 dBm and receiver sensitivity P sen = −90 dBm . The minimum transmitter power for this node is P Tmin = −72.7 dBm − (P S (i) dBm) . The data acquisition node with routing feature is implemented using TI AM3358 ARM processor based board. The analysis of network realtime capability of this board is given in [37]. The link weight (15) is not computed in realtime, but, stored as 3 function table for the variables d GI , P S and b. A simple WSN is established using 1 sink node, 3 data acquisition and routing (APQ) nodes and 1 data acquisition (AQ) node. The nodes uses RCAMR algorithm  Fig. 9 a The analytical value of reliability obtained from DeMoivre-Laplace theorem (35) and binomial theorem (28). The system designed with mttf t F > 25 years has reliability ≥ 0.75 for an initial period of 4.5 years. b The depletion in residual energy of the network after 1000 simulated routing cycles for various algorithms and are programmed to generate 256 bytes of data and transmit in every fixed interval. The data handling capacity for various frame to frame delays is tested and is shown Fig. 10. 100% data delivery is obtained when there is minimum interframe delay of 700 μs . The corresponding power dissipation is also shown in the Fig. 10c.

Conclusion
This paper discusses about the resource constrained wireless sensor networking system for distributed parameter measurement using autonomous routing capability and link fault tolerance. The data processing unit of the sensor node is implemented using low cost IoT platform and the sparse measurement is used for transient voltage acquisition. The sparse measurement based acquisition system gives the advantage of having high transient signal sampling capability at reduced data bandwidth. The high sampling is needed for capturing transient changes in the signal. And the low bandwidth is a desirable feature for the autonomous data routing network implemented using low power WiFi enabled devices. The relaxation based recovery algorithm is used for reconstruction of the transient signal at the data processing station. To make the signal sparse the thresholding of the signal is done prior to acquisition. The ground potential voltage acquired is transmitted to the central data Fig. 10 Number of frame received to number of frames transmitted for various inter frame delay, 10 units of TI CC3200 WiFi processor based data acquisition units are programmed to transmit data frame continuously with inter frame delay of 0.5, 1.0, 2.0 and 2.5 ms. The TI AM3358 ARM processor based beaglebone black (BBB) board is programmed to receive the data frame using RCAMR algorithm. The loss less reception of data is achieved when there is a minimum inter frame interval of 2.5 ms for every data transmission nodes processing system through a network of the wireless sensors nodes, which also function as the routing nodes. Computationally minimalistic routing algorithm is designed and incorporated into IoT based wireless sensor network nodes. The power dissipation is minimized by exploring possible options like adaptive RF power considering the next routing node's sensitivity, routing to node with higher energy backup and data compression capabilities. The link weight computation is stored as look-up table. This adaptive wireless sensor networks can be deployed randomly or orderly in vast area to gather spacial and temporal information. The routing algorithm presented here has fast route discovery and adaptability capabilities. From the analysis it is found that the optimal connection node is 3-5 links away from the data processing node. The WSN scheme for ground potential monitoring presented here has the following advantages (1) minimalistic computational requirement, (2) compatible with low profile IoT platforms, (3) easily deployable, scalable and expendable, (4) failure tolerant autonomous routing capability, (5) reliable and (6) maintains wider the node distribution during power depleted phase. A general model for evaluating the reliability of the multipath resource constrained routing algorithm is also presented. The actual reliability value are calculated from mean time to failure t F determined from accelerated degradation testing of a node. A reliability model for heterogeneous redundant routing network is also discussed. To summarize the paper presents an lightweight algorithm for IoT hardware based wireless sensor network routing for transmitting sparse measurement of transient ground potential measurements.