A Data-Driven Automated Mitigation Approach for Resilient Wildfire Response in Power Systems

The escalating impact of wildfires on critical power systems, including suppression and restoration costs, bankruptcy, loss of lives, necessitates a more sustainable and resilience-oriented response approach. Although power utilities have spear-headed several initiatives, the need for a comprehensive risk management approach that can be easily integrable into current power utility methods and operations cannot be overemphasized. This work proposes a self-sufficient low-cost wildfire mitigation model (SL-PWR), a tool that automates wildfire risk reduction by intelligently functioning from the pre-wildfire phase to prevent wildfires, through the wildfire progression phase for very early detection, to system restoration after damages. Hence, the SL-PWR addresses endogenous and exogenous wildfire mitigation and risk reduction in all system resilience phases, de-compartmentalizing wildfire response. The proposed SL-PWR tool advances on spatio-temporal wildfire detection through data-driven optimization and automation to provide accurate quantitative and visual real-time critical wildfire information to infrastructure operators and emergency management teams. This paper, part of a series, presents the design and development of the SL-PWR’s functional processes, which further enables optimal monitoring for accuracy and rapidity in response, as well as economic decision making of the utility. Results using publicly sourced data from a synthetic utility service area show the performance of the SL-PWR is accurate, enables rapidity, and improves situational awareness during wildfire threats.


I. INTRODUCTION
C RITICAL infrastructure suffer tremendous impact from wildfires.Equipment such as power lines can cause wildfires via faults; conductor-conductor, conductor-ground, conductor-vegetation can cause high-energy arcs, fire, and expulsion embers that act as ignition sources, leading to adverse consequences like bankruptcy [1].The 2021 Dixie fire, started by blown fuses when a Douglas fir fell on a line [2] cost about $630 million, 1500 property damages, and fatalities [3].The the annualized economic burden from wildfires is estimated up to $347.8 billion [4].

II. RELATED WORK
These adverse consequences have led to the study of power grid resilience [5] under wildfire threats [6] as well as the design and implementation of several wildfire mitigation techniques.For instance, wildfire technology and design solution competitions have become fast growing [7].In the academic sphere, artificial intelligence and learning techniques have been applied to (1) wildfire management, (2) wildfire occurrence and risk, (3) wildfire prediction, detection, and mapping, (4) wildfire behavior and spread prediction, and (5) characterization of fuels and wildfire effects.In [8], machine learning is applied on a quantitative dataset given features obtained from satellites.Support vector machines have also been used to detect wildfires from video frames [9].In [10], smoke detection is solved as a segmentation problem using convolutional neural networks (CNNs).In [11], artificial neural networks have been applied to fire detection using features such as heat, light, and radiation, to raise alarms.Satellite imagery has been used for fire and smoke detection [12], [13], as well as vegetation management [14].Unmanned aerial vehicle (UAV) images have also been widely employed in wildfire studies [15], as well as by utilities in wildfire fighting [16].Power utilities have also began employing technologies that anticipate faults that lead to wildfires [17], [18].Similar tools such as the FireALERT MK by Vigilys [19] and the FIRE-Bird [20] have been developed, with certain drawbacks addressed by the SL-PWR.To the best of authors' knowledge, no study has attempted to design and implement a resilience-comprehensive model that intelligently and automatically processes and provides highly crucial information to critical infrastructure operators and appropriate emergency response teams in real-time.In our previous work [21], the spatio-temporal wildfire ignition predictor (STWIP) model is used to study the potential for wildfire ignition, which produces the wildfire potential map of the study area.The STWIP model is integrated with the proposed SL-PWR model according to Fig. 1, where the spatio-temporal wildfire threat maps provided by STWIP is used by the SL-PWR to optimize the UAV operation, presented in the second series of this work.This work follows from our work in [21], going beyond prediction and estimation, further into real-time analysis for prevention, mitigation, and asset management, towards a comprehensive resilient response of the critical power grid to wildfire threats.
Hence, this paper presents the design and development of a novel and intelligent, self-sufficient and low-cost model (SL-PWR) to guide critical power system wildfire response.In particular, the SL-PWR model consists of four major modules: (1) the vegetation module, (2) the power equipment module, (3) the wildfire module, and (4) the burnt equipment module, which are active in all the wildfire resilience phases of the system including pre-wildfire (wildfire analysis), wildfire progression, and restoration phases as illustrated in Fig. 1.The modules are also made up of sub-modules which consist of convolutional neural networks (CNNs) which are used to extract spatial details for detection, classification, estimation, and localization, as the case may be.Specifically, the SL-PWR model as shown in Fig. 1, receives granular mapped spatio-temporal information of wildfire potential in a given service area which has been divided into grid cells with grid centers located at g c .loc with a latitude and longitude (Lat, Lon) at which UAVs can be situated to monitor that particular grid.The g c .locs with high wildfire ignition probabilities are then sent to the SL-PWR for optimizing the UAV trips to these grids to monitor and capture input images.
The SL-PWR performs analysis in real time with computation time that can be easily integrated into power system operations in order to prevent wildfire occurrence.This is achieved via automated vegetation management pre-wildfire, and equipment monitoring during periods of high wildfire threats.If ignitions occur, the SL-PWR aids the accuracy and rapidity of wildfire detection and localization in real-time which enables very early detection and allows the SL-PWR to serve as a first responder which applies firefighting fluid to the localized wildfire boundary.The SL-PWR calculates important details such as fire type, location, spread area, spread rate, and sends the information to appropriate utility stakeholders and emergency response teams in real-time.The proposed model also aids in rapidity of system restoration and transparent inventorying post-wildfire restoration, e.g., the system operator can visualize and get restoration estimates from the SL-PWR's ''Burnt Equipment Detection and Estimation Module''.The SL-PWR is designed to address the gaps that exist in current techniques, methods, and tools, as discussed in the third paper in this series, and introduces additional functionalities e.g., enabling the concept of digital twins in asset management where visuals of the service area provided by SL-PWR during normal conditions can be useful during restoration after damages.The SL-PWR is novelly designed to close the resilience loop, beyond wildfire threat and occurrence phase, and comprehensively connect the resilience pipeline before, during, and after wildfire events.
The rest of this paper is organized as follows.The methodology which introduces the proposed model is discussed in Section III.In Section IV, the SL-PWR is detailed, discussing its modules and sub-modules, and the proposed calculations introduced herein for the image analysis study.The simulation and results are furnished in Section V.

III. METHODOLOGY: INTRODUCING the MODEL
The SL-PWR employs the ResNet18 model as its performance is comparable [22] with other networks, e.g., ResNet34, but with relatively faster convergence.The ResNet18 architecture is as shown in Fig. 2, which is then adapted as required.

A. QUANTITATIVE INPUT DATA FROM STWIP
This section discusses spatial data from STWIP [21] which provides potential ignition locations, visualized as a service area heat map.A spatial location is a point i, located in a grid cell, with geospatial coordinate i.loc.The grid cells are g×g km polygons each with grid centroid with coordinate g c .loc.STWIP provides the g c .loc and their levels of wildfire threat/risk according to the potential ignition probabilities of all i.loc located within the grid, e.g., a grid with high/moderate count of i.loc with high/moderate probabilities within it, is an extreme/elevated risk grid.This information (g c .loc, risk level) is then sent to the SL-PWR operator to be used as input to the UAV navigation for visual inspection and image acquisition.

B. IMAGE ACQUISITION AND PROCESSING
A few databases [8], [21], [23], [24] exist for wildfire detection but these are limited to a smoke dataset [24], NASA's quantitative forecast data [8], image data of wildfire hotspots detected by NASA satellites and the Fire Information for Resource Management System (FIRMS) [23].However, no known database captures SL-PWR input requirements, including utility equipment, wildfire fire-smoke, vegetation type and clearance data.Therefore, image acquisition and processing is a significant effort in the training of the  SL-PWR and thus one of the contributions of this paper is dataset provision [25].Search engines were scraped for RGB image data of different pixels using the SL-PWR python scraper code for image collection while relevant images were retained.The input data consists of over 1800 original images including 863 images, 307 vegetation type images, and 286 images for the burnt equipment detection and estimation module, distributed as illustrated in Fig. 3. Additionally, there are 283 vegetation distance images, and 125 images for fire spread prediction.

1) RESIZE IMAGES
A python function is developed to unify the images and resize them to the input size requirement of the ResNet-18 network at 224 × 224 pixels which have 3 (RGB) color channels.

2) ENCODE LABELS
Samples are labeled with ground truths in supervised training.Categorical labels are transformed to quantitative data points e.g., crown=1, grass=2, litter=3.

3) IMPORT DATA
The datasets are uploaded to google drive from where it is imported into the Colaboratory platform which affords required GPU computation.The data is then sliced into the different categories of the multiple classes.After importing the data, each data class/category is shuffled in order to randomly rearrange the data and avoid bias towards particular classes by utilizing an unbiased data distribution.

4) DATA AUGMENTATION
The slight modification of existing input images using techniques like cropping, color normalization and jittering.Cropping can be applied on (224+x) x (224+x) images and then cropping at fixed (e.g., 4 edges + center) or random locations, to get 224 × 224 images.Also, this can be done by padding images before cropping.Color normalization sets the lowest-highest intensity pixels from values of 0-255 while pixels in all 3 channels are then scaled accordingly.The color jittering changes the image parameters following a normal distribution with zero mean and different standard deviations which change the image brightness, contrast, saturation, and hue, respectively.This gives different contrasts which represent images captured by the UAV at different times and diurnal conditions of the day.Gaussian blur is added for model sturdiness in weather conditions such as fog, mist, etc.These techniques serve to increase input data and also as regularization to reduce overfitting.

5) DATA SPLIT
This function is developed given module requirements to randomly split the dataset to i.) avoid predictability in the dataset and hence overfitting ii.) ensure that bias is mitigated in cross-validation iii.) evaluate accuracy with random data distributions.Here, 100% of the data is in an ''all'' split, 60% in ''train'' split for training, 20% in ''val'' for validation, and 20% in ''test'' testing.

C. METRICS AND LOSS FUNCTIONS
Since stochastic gradient descent is used in training the CNNs, loss functions are selected during model design.according to output requirements of the specific model.

1) L1 LOSS
Also called the Mean Absolute Error (MAE), L1 loss averages all absolute differences between the true value y (i) and the predicted value y (i) .We utilize the L1 loss in (1) because it is not affected by outliers as the L2 Loss.

2) MEAN SQUARE ERROR
The mean square error (MSE) is the L2 loss used to minimize error as the average sum of the all the squared differences between the actual/ground truth value and the predicted value as in (2).In this work, the root mean square is used to evaluate how far away (deviation) the target image's pixels are from the predicted image's pixels.

3) ROOT MEAN SQUARE ERROR
The root mean square error (RMSE) is the square root of the MSE and measures the standard deviation of residuals in the dataset.

4) THE CROSS-ENTROPY LOSS
It is also known as the logarithmic/log/logistic loss, popularly used for classification.In this work, it is used because: 1.) classifications that use sigmoid or softmax activation are more robust with improved performance using the cross-entropy loss [26], 2.) the problems are multi-class classification.The function outputs 1 when the network predicts the correct image and is 0 otherwise.
where y (i) j and y (i) j are the one-hot encoded actual classification and predicted outputs, j is the number of classes (for multi-class), and i represents the data points.Hence, this loss measures the error between the probability distributions.

5) ACCURACY
The accuracy of the multi-class classification is evaluated as in (4) by using the score function defined as the mean of the sum of correct predictions over the sample size N .Similarly, the accuracy of the regression problems is evaluated by using the average L1 distance as in (1).

IV. THE PROPOSED MODEL
The SL-PWR consists of four main modules which include sub-modules that serve to improve system resilience at different phases of the resilience trapezoid [5] as shown in Fig. 1.

A. THE VEGETATION MODULE
Electric utilities perform vegetation management on thousands of miles of overhead lines through tree pruning or removal of vegetation that can interfere with power lines causing arcing/fires, or direct electricity pathways, thus causing wildfires.This SL-PWR module is active in the resilience trapezoid's wildfire analysis phase.In vegetation management, utilities follow standards established by the American National Standards Institute and the International Society of Arboriculture, while the North American Electric Reliability Corporation audits annual vegetation management plans for lines ≥ 200kV, levying fines to ensure standards are met [27].

1) VEGETATION TYPE DETECTION SUB-MODULE
This sub-module aids utility contracted arborists with vegetation management plans, and in mapping fire spread rates.It distinguishes different vegetation types e.g., forests, savannas, shrublands, grasslands, croplands, tundra, which can serve as fuels.To simplify analysis, these are categorized into: Crown, Grass, and Litter, aided by a consulted fire expert [21], which can sustain different types of wildfires including: Crown, Surface, and Ground fires.This grouping can help the fire crew easily recognize vegetation types, fuel characteristics, and fire spread characteristics.The following defines the input data vegetation types as shown in Fig. 4.
a: CROWN This refers to above-ground vegetation including stems, leaves, and reproductive structure, a collection of which forms canopies.It supports Crown fires which spread treetop-to-treetop, at a rapid pace and intensity since the vegetation height exposes those fires to the wind.

b: GRASS
These include grasslands, woody savannas, dominated by grass, supporting Grass fires, often uncontrolled, and can spread to residential and agricultural resources.

c: LITTER
This consists of dead and fallen plant material such as leaves, twigs, that can act as wildfire fuel, usually with lower intensity, rate of spread and easier to put out.

2) VEGETATION CLEARANCE ESTIMATION SUB-MODULE
Vegetation clearance (1) prevents direct contact from line sags/sways causing flashovers when electricity arcs from energized lines to nearby vegetation, (2) allows distance between vegetation and power equipment since trees or tree limbs can fell onto electric equipment, (3) allows vegetation growth management to mitigate direct electricity path to the ground.Vegetation is trimmed along, below, and above power lines as illustrated in Fig. 5, removing tree limbs that are within 8 feet along the sides, 10 feet below, and 15 feet above the power lines [28].Clearance distances are mandated by Occupational Safety and Health Administration (OSHA) and vary with line voltage [27].However, vegetation management typically uses land/air machines, and manual tools which is time-consuming and up to billions of dollars annually [27].

B. THE POWER EQUIPMENT MODULE
This module is active in the Wildfire Analysis and Wildfire Progression phases of resilience as in Fig. 1.In the former, the UAVs inspect power lines in high threat grids or along the assigned travel path, for arcing/flashovers due to electrical faults.Lines can ignite/arc and remain in place after the actions of protective equipment, or can dissociate from overhead poles and contact vegetation to become an ignition source.In the latter phase, we suppose the flashovers contact vegetation, or the line ejects molten particles and starts ignitions, or the arcing remains continuous and provides a sustained source of ignition.For example, in high impedance (HiZ) faults when a single energized line conductor breaks and falls to earth but the resulting fault draws electrical current that is too small to blow a fuse or trip a circuit breaker due to surface contact resistance.A line with HiZ fault can remain energized while on the ground for long time periods producing high-energy, high-temperature arcing.Conventionally, utilities rely on customer calls to detect this condition all while the line could still remain energized on the ground [29].Hence, the module should be able to inform the operator when the equipment risk has become a wildfire ignition.
For this reason, we co-train this module with the wildfire module to detect ''wildfire-fire'', ''wildfire-smoke'', ''wildfire-normal'', ''equipment-fire'', ''equipment-arc'', ''equipment-normal''.The module should be able to differentiate an equipment fire from an actual wildfire ignition as this is crucial for utilities to route appropriate resources.Additionally, the module distinguishes equipment fire from arcing in order to improve utility failure and fault forensics, and enable the operator take adequate corrective actions to mitigate the fault.For instance, power line arcing can be caused by short-circuits which can result from damage/collapse of poles/insulators/line structures, high winds which may cause conductor slap, external conductive objects (e.g., birds, wet objects) resting across live lines.On another note, equipment fire can be caused by component contamination or failure especially during prolonged dry periods.Component contamination can be as a result of a build-up of debris mixing with moisture to create conducting paths within components, which may lead to arcing and eventually equipment fires.Hence, this module can also be applied in the maintenance of power system equipment.

C. THE WILDFIRE MODULE
This module informs the system operator post-ignition during wildfire progression as illustrated in Fig. 1.It aids to i.) detect ignitions/wildfires/under-surface fires, ii.) prepare utility crew routing to affected areas e.g., extra requirements/gear due to heavy smoke, iii.) estimate wildfire spread once ignited.

1) WILDFIRE FIRE-SMOKE DETECTION SUB-MODULE
This sub-module detects the ignition/occurrence of a wildfire.The grid being monitored could be in normal, smoke, or wildfire conditions, hence a multi-class approach is used by adapting the ResNet-18 as in Fig. 2. It is co-trained with the power equipment fire-arc detection to improve robustness in distinguishing actual wildfire ignitions from fires/arcs captured on power equipment but have not yet caused an ignition.

2) WILDFIRE LOCALIZATION AND SPREAD ESTIMATION SUB-MODULE
This predicts the wildfire boundaries using bounding boxes and then calculates the radial spread using the box coordinates.Hence, it performs two main functions: 1.) localizes the wildfire in the grid and 2.) calculates wildfire spread area.It also enables a third function, which is 3.) calculating the rate of spread of the wildfire in real-time.The network architecture for this sub-module is illustrated in Table 1, where the fully connected layer is modified to an input of 512 neurons with an output of 4 neurons which represent the wildfire bounding box coordinates to be detected.The 4 neurons indicate fire height h f , fire width w f , fire boundary positions on the x and y axis, x f and y f respectively, in a 2dimensional grid, where the UAV captures the wildfire image from above the grid.
Importantly, this calculation takes into account the scale of the UAV image to the actual size of the grid at any height level at which the UAV captures the image, since this height influences the wildfire localization and spread calculation, as illustrated in Fig. 6.Hereon, the localization model is then developed assuming radial spread and hence an ellipse,   as represented in (5), inside or outside the predicted bounding boxes is as illustrated in Fig. 7.
where x = a cos θ and y = b sin θ and the considered ellipse is centered at (x + w 2 , y + h 2 ) where w and h are the height and width of the box, respectively.The ellipse circumscribing the bounding box should be used when boxes are labeled conservatively (box does not quite enclose fire area) then the area of the spread/ellipse should be assumed largest when sin 2θ = 1.However in this work, the labeled box coordinates adequately enclose the wildfire location and hence the inscribed ellipse technique is utilized as detailed.Let a − 0 = A and b − 0 = B in Fig. 7, then the area of the ellipse is: Now assume that the wildfire bounding box is located in an image which is a scaled version of the original grid, i.e., UAV distance to ground level decreased during image capture, hence the captured image is magnified in comparison to grid, as in Fig. 8.Then, in order to scale the wildfire bounding boxes with height and width h f and w f respectively, to the original image, the following relationship is defined mathematically as: where Area b_box is the scaled area of the wildfire bounding box with height and width w f and h f as illustrated in Fig. 8.
Then assuming radial spread as illustrated in Fig. 7, the spread area S Area is calculated as in (11).
Furthermore, this sub-module can inform wildfire spread rate in real-time which is indispensable to improving situational awareness given the dynamic nature of the parameter which could be exacerbated or otherwise by weather conditions.Mostly, mathematical models are developed to calculate fire spread rate, however, spread rate can be unique to certain geographical attributes not represented in pre-defined mathematical models (e.g., spread rate changes with slope/landuse), making preexisting models less accurate for real-time estimation.Hence, the SL-PWR's wildfire localization and spread detection module can minimize dependence on mathematical models, vegetation models, or quantitative data.
The spread rate can be calculated as in (12), by getting the fire spread area at different time stamps that the UAV captures.
where S ′ Area t and S ′ Area (t−1) are the farthest point towards the direction of wildfire spread at time t and t − 1, respectively.

D. THE BURNT EQUIPMENT DETECTION AND ESTIMATION MODULE
This module is active in the restoration phase where equipment suffers damages after fire suppression.Conventionally, utilities route inspection crews to the burnt service area to estimate damage and thus, restoration costs [30].With this module, UAVs can enable cost and time efficiency by reducing inspection crew needed.Another advantage is the provision of actual equipment images and hence transparency in cost estimation.The architecture consists of a damage type detection network as in Table 1, with fully-connected and softmax layers having 3 neurons detecting: 1.) top/cross arm damage, 2.) pole base damage, and 3.) leaning pole damage.The estimation network for each damage type consists of convolutional layers which take in positively classified images and culminate towards predicting a scalar that informs the extent of burn damage as in Table 2, where the layer 5 convolution is modified from 512 channels to 1 channel, and then 14 × 14 average pooling is performed yielding the burn damage scalar value.The logic for labelling the ground truth for different burn damage scenarios as illustrated in Fig. 9.

1) CALCULATING BURNED POLE PARAMETERS
Pre infrastructure restoration, UAVs capture burned equipment images.Image height parameters are mapped to the real equipment, as in Fig. 10, using references of known height e.g., pole tags widely used by power utilities.The pole height can be calculated as: where H T is the actual equipment height, H p T is the measured equipment height in the image, H R is the actual reference height, and H p R is the measured reference height in the image.The objective is to estimate the height of the pole base to be bolted-on, as in ( 13), since it is more economical than disconnecting parts of the service area and possibly downstream customers, then replacing and re-wiring.
where H bolted is the estimated height of the burnt base to be bolted-on, H p T burnt is the measured height of the remaining top part of the equipment from the captured image, and L is the total of the margin of error + the part of the pole that goes underground for the foundation of the equipment.

b: LEANING POLE
If angle of tilt ϕ passes a certain utility threshold, repair crew are routed to prevent sags, breakage, or external contact, in the line.In order to estimate the height difference between normal and leaning poles, the previous equation is adapted given Fig. 10, where the height difference H D is calculated as in ( 15) and H T p leaning is the measured height of the leaning pole in the image.
Furthermore, ϕ can be estimated directly from the captured image or can be calculated albeit more rigorously where ϕ = σ , the angle made by the line parallel to the leaning part of the pole at the baseline with length b and perpendicular to the slope with distance s, θ is the angle of view of the camera mounted on the UAV and is calculated as follows.
where S W is the sensor width also known as the width of the camera film (these are standard for different camera types),  F L is the focal length of the camera lenses, and (180/pi) aids the conversion between degrees and radians.In practice, it may become problematic to position the UAV as in Fig. 10 to calculate σ as 90 • − 90 • − θ 2 , hence close approximations can be made by ''eye-balling'' the images.

c: ATTACHED CROSS-ARM EXTENSION
This scenario can be caused by crown fires, and equipment fires/arcing.Here, it would be economical to attach cross-arm extensions, replacing burned parts as shown in Fig. 9.The equation is as follows: where H p T base is the measured height of the remaining unburnt part of the power equipment.Here, the parameter L is eliminated since the margin of error can easily be compensated for using e and there is no need for estimating the height of the equipment to be buried towards the equipment foundation.

V. SIMULATION AND RESULTS
Three major data augmentations are applied including fivecrop, random flipping and color jittering.Prior to the five-crop, images are padded to 235 × 235 and then cropped at the four edges and center to a final 224 × 224 size.The hyper-parameters are set after cross-validation using random layout [31], such that distinct function values are visited during hyper-parameter optimization as illustrated in Fig. 11.The best performing learning rates during validation are chosen.The model, summarized in Table 3, shows rapid detection of less than 40 milliseconds once the UAV images are captured.This rapid detection is crucial in fire fighting, 672 VOLUME 10, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.as every second matters.The model is trained on the Tensor-Flow framework using Google Colaboratory with designated GPU runtime.For all the modules, the dataset is split into 6   10   for training data, 2  10 for validation data, and 2 10 for test data.

A. THE VEGETATION MODULE
In training this network, the Adam optimizer is used with a learning rate of 5×10 −5 , while a batch of 64 images is trained over 25 epochs.Fig. 12 shows the sub-module performance, where the validation and test accuracy is 93.4% and 91.8% respectively.The detection accuracy for litter is 90%, grass is 87% and crown is 100%.Similarly, the minimization of the cross entropy loss improved over epochs.Furthermore, Fig. 13 shows the complications in the mispredicted vegetation types.For instance, the second misprediction was labelled crown and predicted grass, however, its classification is difficult from the distance of image capture.In these cases, vegetation with higher growth/spread rate can be chosen as the predominant label.The second sub-module estimates a scalar value of vegetation clearance from power equipment.
The level of clearance is on a scale of (extreme = 0.1, elevated = 0.5, normal = 0.8) depending on the closeness of the vegetation to the power lines.The Adam optimizer is used with learning rate of 2 × 10 −5 , and a batch size of 32 trained over 100 epochs.The estimation losses are minimized as in Fig. 14.

B. THE POWER EQUIPMENT MODULE
This is co-trained with the fire-smoke detection sub-module using Adam optimizer with a learning rate of 5 × 10 −5 and a batch size of 64 images trained over 25 epochs.It's performance is shown in Fig. 15, with 89.60% test accuracy.Next, the module's mispredictions are furnished in Fig. 16, to understand how to better improve the network.Generally, performance is relatively worse with darker augmentation i.e., simulating night time.For instance, differentiating equipment fire and arcing in the first image since both are bright reddish at night time.The contrast which emulates sunrise in the second image is seemingly confused for arcing.This highlights the need for night vision UAV cameras and also visually verifying images for which the SL-PWR raises an incident alarm.These mispredictions can be improved or even mitigated with more training data samples of these incident types.

C. THE WILDFIRE MODULE
The wildfire fire-smoke detection sub-module is co-trained with the equipment module with prediction accuracy for individual classes furnished in Fig. 18, where all normal conditions are detected reducing false positives.With the wildfire fire and smoke, accuracy is > 90%, while the equipment fire and arcing about 90% and 75%, respectively.This performance can be improved by increasing samples (Fig. 3 shows the equipment arcing samples are barely 7% of the input data).Next, the wildfire spread labeled as discussed in (11).The network is trained with Adam optimizer, a learning rate of 2 × 10 −5 and a batch size of 32, over 100 epochs.The performance of the spread estimator in Fig. 19 shows the minimization of estimation losses over epochs with 0.01166 average test data MSE.Also, it's mispredictions can be visualized in Fig. 20, e.g., in the first image, the ground truth is 0.044 while the prediction is at 0.032.Furthermore, the wildfire localization estimator is trained with Adam opti-

D. THE BURNT EQUIPMENT DETECTION AND ESTIMATION MODULE
To label input data, poles are assumed 12m long and buried 2m underground as per US standards1 as in (18).
where L estimate is the length estimate of the burnt off pole part, n is the length of the burnt off pole part in the image, h is the height of the entire pole in the image, and 14m is used for the bolted-on base scenario given the 2m pole-burying height.
The angle of tilt/lean is measured with a protractor during labeling, since images obtained from search engines do not have any specific position/height/angle of capture and hence calculating σ will not suffice.During training, the image dearth from search engines, for scenarios in Fig. 9 led to a high risk of overfitting as observed from Fig. 23. and hence, additional data augmentation including flipping, gray scaling, and color jittering is applied.Random affine transformation is also used to preserve points, lines, and planes, hence aiding to correct for geometric distortions that occur with non-ideal camera angles.

VI. CONCLUSION
This paper discusses the design and implementation of the SL-PWR wildfire mitigation model that uses optimized spatio-temporal data to detect and localize wildfires in real-time.The SL-PWR also provides critical information before, during, and after wildfire events, for comprehensive resilience.Before ignition, the SL-PWR's vegetation module is active to automate vegetation management.During high threat periods, the power equipment module is active to mitigate endogenous wildfires.If ignition occurs, the wildfire module aids detection, location, and containment of already progressing wildfires, while the burnt equipment module is active for system restoration.Results show that SL-PWR's modules perform these functions accurately, further aiding ''very early wildfire detection'' with several functionalities.For instance, the SL-PWR serves as first responder by applying firefighting fluid, containing the fire to the localized area and preventing loss of lives.Further work discusses optimization of SL-PWR's monitoring, and it's economic viability compared to other existing methods.

APPENDIX A THE STRUCTURE Of THE CNN
The CNN is the fundamental network used in obtaining spatial attributes used to train the SL-PWR model.It is a deep learning algorithm that takes in an input image and assigns learnable parameters (weights and biases) to various aspects/elements of the image so as to differentiate one image from another.It is a multi-layer neural network that consists of convolution layers, pooling layers and fully connected layer as illustrated in Fig. 24.The convolution layer(s) are made up of N @ F × F filters which basically translates to a matrix of weights called feature maps.In order to generate these feature maps, the filters (a pre-defined matrix initialized with height and width parameters) travel left to right on the input image/map, stepping in strides of predefined width and taking the dot product of the applied filter/kernel and the image/feature map area overlapped by the filter, after which it moves downward with step size of a predefined stride height and repeats the step across the image (i.e., from left to right).
The CNN operator at each layer is completes the following function.
where the layer under consideration is i, j is the feature map under consideration in layer i, Y x, y ij is the output located at position ( x, y) in feature map j and layer i, A(•) represents the layer's activation function, b ij is the bias term, ω pq ij denotes the weights/value of the convolution filter (F ×F), at position (p, q), associated with layer i and feature map j.In the event where the filter size and stride would leave certain parts of the input unattended, padding can be applied.This creates the output volume from each convolution layer given the filter size, padding, and stride, according to (20), where I is the input volume of the I × I image, F is the kernel size (volume of the filter, [F < I ]), P is the padding and S is the stride.Hence, by convolving the filters with the input image and carrying out non-linear transformations using activation functions, N feature maps are created.The activation function adopted in the proposed model is the ReLU (Rectified Linear Unit) function as in 21.
The pooling layer(s) performs it pooling operation by obtaining the average or maximum value of the elements of the feature map where its window slides, given the kernel size (height and width) of the filter and the strides.Hence, this layer extracts the dominant features, a dimensionality reduction of sorts which also helps to improve computational efficiency.Together, the convolutional layer and the pooling layer form the i th layer of the CNN.The fully connected layer is one that learns the non-linear combinations of these high-level features as transformed by the convolutional layer, hence, learning a non-linear function.It takes in the elements of the feature maps feeding directly into it and then flattens these elements towards the output which could be classification or regression type.The flattened elements are then fed into a feed-forward neural network, learning the parameters (ω, b) by minimizing the negative log-likelihood given the training input as in (22).

L(ω, b) = −
where I k is the correct (target) class label for the input image under consideration.This objective is optimized by applying applying stochastic gradient descent with back propagation using the chain rule as in (23), to training iterations over several epochs.
where µ is the learning rate, N i is the total number of layers in the network, Y n i is the output of layer i during iteration n.With this process, the model is then capable of distinguishing dominant and less-superior features in the input images, further classifying them using the Softmax function, an adaptation of the Sigmoid function used for multi-class classification, which takes in the vector of R real numbers and normalizes them into a probability distribution of N probabilities which are proportional to the input exponentials as in (24), where f c (I k ; (ω, b)) is the scores from each of the multiple classes of interest c ∈ {1, • • •, N } transformed into conditional probabilities using the Softmax function which applies the exponential function to the elements of its input vector and divides the obtained value by the sum of the exponentials of all elements (normalization) which ensures the output components sum up to 1.In order to test the CNN model after the training process described above, the output layer then predicts the label I of the image input I using the argmax of the Softmax-transformed probabilities as in (25).
The proposed SL-PWR consists of sub-modules which are built fundamentally based on the Residual Neural Network (ResNet18).

1) THE ResNet18 CNN MODEL
ResNet18 has been widely applied to different image vision and classification problems as it provides a solution to the issue of vanishing gradients, which occurs as continuous multiplication during back-propagation makes the gradients infinitesimal as neural networks get deeper [32].As illustrated in Fig. 25, the block tries to learn an output, say G x .The residual block allows the network to directly learn F(x) = G(x)−x, such that the target output is F(x)+x hence avoiding depreciating performance that having too many convolutional layers would have introduced.For instance, in the block in Fig. 25, the residual mapping function is as in (26), while the output of the block after the second ReLU activation is as furnished in (27).
where σ is the ReLU activation function.Given the ''identity shortcut connection'', the network can skip one or more layers in order to avoid performance degradation birthing different variants including the ResNet18 and ResNet34 proposed in [32].

FIGURE 1 .
FIGURE 1.The Self-Sufficient Low-Cost Power System Wildfire Resilience (SL-PWR) Model.Illustrating resilience trapezoid wildfire phases mapped to the SL-PWR modules, from pre-wildfire phase to wildfire progression phase to post-wildfire phase.

FIGURE 2 .
FIGURE 2. ResNet-18 Architecture: Illustrating the modification zone for the classification and wildfire localization problems.

FIGURE 3 .
FIGURE 3. Visualizing module data samples and distribution.

FIGURE 5 .
FIGURE 5. Vegetation managements specification for scheduled maintenance considered in SL-PWR's vegetation clearance estimation sub-module.

FIGURE 6 .
FIGURE 6. Illustrating the UAV-height-informed scaling for radial spread calculation.In the figure, a signifies the area of fire spread, and as the UAV's distance from the ground increases, the spread area in the image proportionally reduces by nx signifying the UAV's distance-from-ground.

FIGURE 8 .
FIGURE 8. Calculating wildfire spread: illustrating the scaling to grid area when the distance of the UAV to ground level varies by the parameter ''a''.This is synonymous to ''zooming in''.

FIGURE 9 .
FIGURE 9. Ground truth labeling in the burn damage detection and estimation module scenarios.First: burnt pole base where it is more economical to bolt-on a base to avoid re-wiring.Second: pole is leaning when distended from the normal where repair crew can add support along the pole length.Third: burnt cross arms where attaching cross arm extensions will suffice.

FIGURE 11 .
FIGURE 11.Random search during hyper-parameter optimization ensures that more of the hyper-parameter space is visited.

FIGURE 13 .
FIGURE 13.The mispredictions of the Vegetation type module.

FIGURE 23 .
FIGURE 23.Performance of the burnt equipment module.

FIGURE 24 .
FIGURE 24.The architecture of a convolutional neural network.
I k ln p(I k |I k ; (ω, b))

FIGURE 25 .
FIGURE 25.Implementation of the identity shortcut connection via the residual block.