Determining forces exerted on a structure based on the resulting deformation

Abstract

A computer implemented system configured for receiving obtaining sensor data comprising one or more displacements as a function of time of one or more targets attached to a structure in response to point loads applied to the structure; optionally receiving image data representing images of the vehicles comprising the point loads traversing the structure; and determining, from the displacements, at least one of a health status of the structure, or forces applied by one or more of the point loads.

Description

[0001] DETERMINING, IDENTIFYING, AND DISTINGUISHING THE FORCES EXERTED ON A STRUCTURE BASED ON THE RESULTING DEFORMATION AND A CALIBRATION PROCEDURE FOR THE SYSTEM AND A METHOD TO CALCULATE THE FORCES FROM THE OBSERVED DEFORMATION AND INFERRING CHANGES IN THE VARIABLE CHARACTERISTICS OF THE STRUCTURE CROSS REFERENCE TO RELATED APPLICATIONS This application claims the benefit under 35 U.S.C. Section 119(e) of the following U.S. Provisional Applications: Serial Number 63 / 548,393 filed on November 14, 2023 by Shervin Taghavi Larigani, entitled “Determining, identifying, and distinguishing the forces exerted on a structure based on the resulting deformation and a calibration procedure for the system and a method to calculate the forces from the observed deformation”; Serial Number 63 / 633,607 filed on April 12, 2024 by Shervin Taghavi Larigani, entitled “A Versatile System for Detecting Applied Forces on a Structure and Monitoring its Structural Health”; Serial Number 63 / 640,820 filed on April 30, 2024 by Shervin Taghavi Larigani, entitled “A Versatile System for Detecting Applied Forces on a Structure and Monitoring its Structural Health”; and Serial Number 63 / 678,497 filed on August 1, 2024 by Shervin Taghavi Larigani, entitled Determining, identifying, and distinguishing the forces exerted on a structure based on the resulting deformation and a calibration procedure for the system and a method to calculate the forces from the observed deformation and inferring changes in the variable characteristics of the structure; all of which applications are incorporated by reference herein. Further information on sensor systems / devices and methods for measuring displacement time series, as well as methods and systems for determining weight distribution of point loads from the displacement time series, can be found in US patent application serial number 18 / 833,159 filed on July 25, 2024 by Shervin Taghavi and entitled “NEW NON-INVASIVE FULLY AUTOMATED SYSTEM IDENTIFYING AND CLASSIFYING VEHICLES AND MEASURING EACH VEHICLE'S WEIGHT, DIMENSION, VISUAL CHARACTERISTICS, ACOUSTIC PATTERN AND NOISE IN REAL-TIME WITHOUT INTERFERING WITH THE TRAFFIC, which application claims the benefit as a national stage entry under 35 USC 371 of international application serial number PCTUS2361291 filed January 25, 2023 (published with publication number WO 2023 / 147375 published on August 3, 2023 , which application claims the benefit under 35 U.S.C. Section 119(e) of co- pending and commonly-assigned U.S. provisional patent application Serial Nos. 63 / 302,964, filed on January 25, 2022, by Shervin Taghavi, entitled “NEW NON-INVASIVE AUTOMATED SYSTEM TO MEASURE VEHICLE’S WEIGHT, DIMENSION, AND NOISE IN REAL TIME WITHOUT INTERFERING WITH THE TRAFFIC,”and 63 / 368,652, filed on July 17, 2022, by Shervin Taghavi Larigani, entitled “NEW NON-INVASIVE FULLY AUTOMATED SYSTEM IDENTIFYING AND CLASSIFYING VEHICLES AND MEASURING EACH VEHICLE'S WEIGHT, DIMENSION, VISUAL CHARACTERISTICS, ACOUSTIC PATTERN AND NOISE IN REAL-TIME WITHOUT INTERFERING WITH THE TRAFFIC; and 63 / 407,662, filed on September 18, 2022, by Shervin Taghavi Larigani, entitled “METHOD FOR DETERMINING THE NUMBER OF AXLES, AXLE WEIGHTS, AXLE SEPARATIONS, AND VEHICLE SPEED AS WELL AS A METHOD FOR DETERMINING IF A VEHICLE’S MAXIMUM STRESS ON THE ROAD EXCEEDS THE PERMITTED LIMIT USING THE MOTION THAT THE VEHICLE INDUCED ON THE BRIDGE AS IT TRAVERSES”; and All of which applications are incorporated by reference herein. BACKGROUND OF THE INVENTION 1. Field of the Invention. The present disclosure relates to methods and systems for monitoring vehicles and structures. 2. Description of the Related Art. What is needed is a less invasive method for measuring health status of civil structures, industrial complexes, and characterizing vehicles (e.g., weight distributions of vehicles traveling on public freeways). The present invention satisfies this need. SUMMARY OF THE INVENTION A computer implemented system comprising: (a) a computer having one or more memories; (b) one or more processors executing on the computer; (c) the one or more memories storing a set of instructions, wherein the set of instructions, when executed by the one or more processors cause the one or more processors to perform operations comprising: receiving obtaining sensor data comprising one or more displacements as a function of time of one or more targets attached to a structure in response to point loads applied to the structure; optionally receiving image data representing images of the vehicles comprising the point loads traversing the structure; determining, from the displacements, at least one of: a health status of the structure, or forces applied by one or more of the point loads by: obtaining a model for the displacements as a function of a forces applied by the point loads, wherein the model models the displacements as a superposition of responses of the structure to the one or more point loads at each of one or more coordinate locations in a virtual coordinate grid associated with or on the structure; and solving or deducing the model for the forces as an inverse problem using the coordinate locations of the point loads and the displacements obtained from the image data and the sensor data respectively. BRIEF DESCRIPTION OF THE DRAWINGS The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee. Referring now to the drawings in which like reference numbers represent corresponding parts throughout: Figure 1:detecting the weight on each wheel of a train (or also individual axle weight) deflection that it causes as it traverses a bridge Figure 2:detecting the weight on each wheel of cars from the displacement of the bridge that they traverse Figure 3: detecting the weight on each wheel of an air plane from the deflection that it causes as it traverses an airplane bridge Figure 4:An image of a standard road reflector that could be used to track road movement as vehicles pass over it. Figure 5: An image of a standard road reflector that could be used to track road movement as vehicles pass over it. Figure 6:Road marking paint that could be used as visual target Figure 7:Road marking paint that could be used as visual target Figure 8: illustrates the practical application of the curve fitting method with a vehicle traversing a bridge during testing conducted with the Kansas State Police Figure 9A: 2D Grid Representation of the surface of the bridge: Each Arrow Represents a Point Force Applied at Specific Locations. Figure 9B shows the displacement of the visual target that is measure is the combination of the displacement induced by each single load on the bridge. Figure 10: It is a screenshot of the algorithm running on our computer, showcasing one example of the implementation; however, this is not the only possibility, as it describes the situation where, as a vehicle enters a Region Of Interest, its image is extracted allowing it to identify the precise position of each wheel on every vehicle; armed with this information and knowing the location of each car at any given moment, we can reconstruct the position of each individual wheel at each instant on. Likewise, we can Likewise, we can capture a vehicle's DOT number and plate as it enters a region of interest Figure 11: This figure is another screenshot from our computer, now depicting a truck entering the scene. Likewise, we can Likewise, we can capture a vehicle's DOT number and plate as it enters a region of interest (ROI). Figure 12:illustrates one embodiment of the program flowchart; however, this figure is exemplary and should not be interpreted as limiting. Figure 13: Initialization step using Graphical User Interface Figure 14a: A traffic camera images at one of the busiest congestion points in the U.S., where the 210 Freeway connects with the 134 Freeway. The camera tracks and monitors all vehicles traveling in both inbound and outbound directions. Figure 14b. Program architecture. Figure 14 c. Vehicle suspension schematic. Figure 14d. Health monitoring system schematic. Figure 15:A times series of bridge displacement, and a close-up view of the displacements, illustrating our measurement sensitivity to detect individual vehicle axle loading. This figure shows the time series displacement of a visual target on a freeway bridge using real-time video images from a camera, while applying our algorithm to compute the displacement of the visual target in real time. Figure 16: power spectrum density of the time series data show in figure 1. We can observe the resonances of the bridge Figure 17a:This image shows a rail where we can select any visual target to monitor the deflection in order to deduce the point load of traversing train-cars. Figure 17b. Image or rail. Figure 18: this is a video images where (1), (2), (3), (4) are the location of the visual targets that we have been monitoring Figure 19 Live video feed displayed to passenger. In one embodiment, but not limited thereto, the same camera may be utilized for the application or for a camera positioned in a similar location. Figure 20. Method of monitoring (e.g., health status of) a power plant. Figure 21. Schematic of a steam power plant generating electricity by using steam that can be monitored using the methods described herein, wherein the plant performs 1, Heating Water: (the plant heats water in a boiler by burning fuel which creates high-pressure steam) 2. spinning the turbine (the high-pressure steam flows into a steam turbine and the steam makes the turbine blades spin); and 3. Generating Electricity (the spinning turbine is connected to an electric generator, and As the turbine spins, it turns the generator, which produces electricity. Figure 22 is a schematic of a power plant, showing in a thermal power plant, steam flows over turbine blades, causing the turbine shaft to rotate, the rotating shaft is connected to the generator shaft, which converts the mechanical energy into electrical energy through electromagnetic induction; turbine Shaft (steam causes the turbine blades to spin, which rotates the turbine shaft; and generator shaft (the rotating turbine shaft turns the generator shaft, which converts mechanical energy into electrical energy). Figure 23 illustrates a generator in the power plant. Figure 24 is a schematic illustrating the generator can be represented as a mass-spring-damper system. In this model, a mass M is attached to a spring that exerts a restoring force proportional to the displacement from its equilibrium position, according to Hooke's Law. The system is characterized by the following parameters: M for the mass of the generator, kx, kyfor the spring stiffness along the x and y axis; and Cx, Cyfor the damping along the x and y axis, Fx is External force applied by the turbine shaft to the generator along the axis of rotation of the shaft and Fy is External force applied by the turbine shaft to the generator perpendicular to the axis of rotation of the shaft Figure 25 illustrates any change in the orientation of the turbine blades relative to the shaft axis creates torque along the turbine shaft, causing changes in the external forces on the generator leading to upset the Mass-spring-damping system. Figure 26 illustrates target monitoring locations including a visual target 2600 located on the generator casing, which is physically attached to the generator and a visual target 2602 located at the interface between the turbine shaft and the entrance of the generator. Figure 27 illustrates a model of an electric engine. Figure 28 illustrates an example system set up in the field for monitoring a civil structure. Figure 29 illustrates deployment of the system in the field. Figure 30 illustrates the system a real-time traffic analysis algorithm also identifies individual wheels and axles of a vehicle, and distinguish those that are raised and not in contact with the ground. Figure 31 illustrates the system of Figure 28 set up 1 km from the civil structure comprising a bridge, so as to monitor the bridge. Figures 32a-32g illustrate different camera set ups relative to a bridge. Figure 33 illustrates measurement of a time series deflection of a target on a short stiff bridge. Figure 34 illustrates identification of passage of various sized vehicles on a rigid and short bridge, where we can not only clearly observe the passage of trucks but also have enough signal-to-noise ratio to distinguish the passage of lightweight vehicles, such as passenger cars. Figure 35. Time Series displacement of a target in response to passage of vehicles on a bridge, along with zoomed in view. Figure 36. Time series displacement of a target in response to passage of trucks on an interstate highway overpass. Figure 37. Zoomed in view of time series displacement of a target in response to passage of trucks on an interstate highway overpass. Figure 38. Time series displacement of a target in response to passage of trucks on an interstate highway overpass showing bridge free vibration oscillation that can be used to monitor health status. Figure 39. Monitoring the deflection of the Gold Line Metro in Los Angeles, where all train cars have the same weight when there are no passengers. The deflection changes are attributed to variations in passenger volume. Figure 40. measurement of out of plane displacement of each visual target identified 1 and 2 on the airplane wing of Fig.18. Figure 41. Normalized out-of-plane displacement power spectrum density of (1) and (3) targets on the wing of Figure 18. The turbulence creates a quasi-periodic motion in the wing, leading to a pseudo-periodic movement marked by a prominent peak in the power spectral densities. This peak differs from the structural resonances that occur at higher frequencies ─It's important to note that this observation is based on a very short measurement period. In contrast, gathering data over a longer time span would result in a power spectral density with a more defined profile and much better structural resolution Figure 42. Example hardware environment. Figure 43. Example network environment. Figure 44. Example System. Figure 45. Example System according to another embodiment. Figure 46. Example Neural Network. Figure 47. Example coordinate grid. Figure 48. Flowchart illustrating a method of monitoring vehicles and / or structures. DETAILED DESCRIPTION OF THE INVENTION In the following description of the preferred embodiment, reference is made to the accompanying drawings which form a part hereof, and in which is shown by way of illustration a specific embodiment in which the invention may be practiced. It is to be understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention. Technical Description Overview of Technology A system according to embodiments described herein is composed of several primary components: 1. A unit configured to measure and calculate, in real time, the dynamics and transients of a target structure. 2. A unit configured to identify and track, in real time, the point load applied to the target structure. 3. A computation unit configured to receive information from the aforementioned units and to calculate, in real time on or more of the following: a. the solution to the inverse problem of assigning an intensity value to each point load. b. computations related to the health monitoring of the target structure. In this scenario, the system could perform additional calculations using data from a weather station, broadening the scope and depth of the analysis to make it more thorough and comprehensive. 4. A server or remote computation unit configured to receive information from the previous computation unit and to display the processed information on a web application in real time. The term "system" as used herein refers to, but is not limited to, a configuration that includes at least one sensor and computational components designed to measure and calculate the dynamics and transient behavior of a structure. For example, in one case, this system could consist of measuring displacement time- series data, thereby providing real-time insights into the structural performance and response under dynamic loading conditions. The term "sensor," as used herein, refers to, but is not limited to, any device or system capable of detecting or measuring displacement. Examples of such sensors include, without limitation: laser-based sensors, range finders (including those utilizing Doppler effects or phase-based detection methods), vision-based measurement system, seismometers, accelerometers, and other similar or equivalent devices. A "point load tracking and identification system" is a system that identifies and tracks at each measurement instance the location of individual point load applied to the structure. A system configured to identify and track, at each measurement instance, the location of individual point loads applied to a structure may be referred to as a "point load tracking and identification system" or "load monitoring system." Specifically, if it uses sensors or cameras for this purpose, it could also be described as a "real-time point load detection and tracking system." A system for collecting real-time data from the system units described in 1) and 2) and for deducing the intensity of each individual load is referred to as a "real- time load monitoring and intensity deduction system. This system integrates data from the real-time displacement measurement system and the point load tracking system to calculate or infer the intensity of each applied load on the structure at each measurement instance. The computation, as described herein, may be performed in a distributed manner across different platforms. This includes, but is not limited to, performing data processing and analysis on multiple devices, servers, or cloud-based platforms. Each platform may be responsible for specific computational tasks, such as processing sensor data, calculating displacement, tracking point loads, or deducing load intensity, which can then be integrated to provide a comprehensive real-time analysis of the target structure's behavior. The term "structure," as used herein, refers to, but is not limited to, any civil structure, such as buildings, bridges, or infrastructure, as well as any other object or system where displacement and load monitoring may be applicable. This includes, but is not limited to, mechanical components, vehicles, industrial equipment, or any other physical object subjected to load or displacement. In one embodiment, the structure consists of a bridge. In this embodiment, the system is configured to monitor and measure the real-time displacement of the bridge and track the location and intensity of point loads applied to the bridge, such as those caused by vehicles, pedestrians, or environmental factors. By "vehicle," as used herein, we refer to, but are not limited to, any form of transportation that moves on or across the structure, e.g. as illustrated in Figs.1-2. This includes, but is not limited to, motorized vehicles such as cars, trucks, buses, motorcycles, and construction machinery, as well as non-motorized vehicles such as bicycles or carts. The term may also encompass rail vehicles, such as trains, in cases where the structure includes or supports railway infrastructure. By "vehicle," we also include airplanes taxiing on the runway as illustrated n Fig.3. This encompasses any form of aircraft that moves on the ground, including commercial airliners, cargo planes, and general aviation aircraft. The inclusion of airplanes in this definition highlights the system's capability to monitor and measure the impact of various vehicles, both terrestrial and aerial, on the structural integrity and displacement of the monitored structure, such as a bridge or runway. Embodiments of the present invention may also be applied to aircraft or airplanes in flight. In the case of vehicles, a 'point load' refers to the individual force that each wheel-suspension system imparts on the structure. Example point loads include contact points (e.g., wheels) between a vehicle and the structure applying force to the structure, or other subcomponents (e.g., fuel tank in an airplane wing, turbine blade, generator casing ) of a vehicle or structure. Embodiments of the present invention are discussed in the following sections. 1.1 Utilizing Road Movement to Determine Point Loads Instead of a Bridge A method for measuring the dynamic characteristics and transients of a road surface, comprises the steps of utilizing the movement of a target on the road as vehicles traverse said road to determine the weight distributed on each wheel of each vehicle In another embodiment, the target structure is the road, and we are examining the displacement caused by traversing vehicles, by continuously tracking the movement of stationary visual targets on the road such as road markers and pavement reflectors by employing specialized techniques and sensors, such as cameras or other sensor suites As an example in the case of the camera, the camera continuously captures images, and we monitor the displacement of the object by calculating its position within the camera frame. Figs.4-7 illustrate we can use any road marking paint on road surfaces (including also airplane tarmacs) and monitor its motion relative to an inertial reference frame to assess road movements, dynamics, and transients as vehicle traverse by to deduce their weights. In one embodiment, a physical apparatus comprises a strategically positioned camera, with the camera location considered as an inertial reference frame relative to the target road. The camera is oriented to focus on a designated area where a visual target resides within its field of view. This positioning enables the continuous recording of the movement of the target. In one embodiment, a specialized layer of pavement is applied to the road surface, featuring the optimal level of firmness, specifically designed for our application, which involves measuring the displacement of targets on the road to deduce the forces applied to the surface, as described in this manuscript. Pavement can be precisely engineered to undergo a small, controlled deflection as vehicles pass over it, much like a bridge bends under weight. This deflection helps evenly distribute the load across the underlying layers, ensuring the pavement returns to its original shape once the load is removed. The degree of deflection is carefully managed through the selection of materials, layer thicknesses, and the overall structural design. Pavements are constructed with specific materials and structural layers to optimize their response to loading forces. The goal is to create a controlled deflection that spreads the load across the layers below, enhancing the pavement's resilience and durability. Advanced materials, such as flexible asphalt mixtures, reinforced concrete, and others, are commonly used in these designs to improve performance and ensure long-term durability. In one embodiment, the specialized layer of pavement is a separate layer of pavement / road material that deflects in a predictable manner (e.g., proportional to force) under load rather than absorbing the force, and restores to the original shape after removal of force / deformation. Example materials include, flexible or.elastic material (rubber, steel, elastic pavement) 1.1.1 Inferring individual wheel weight from measurement: We address the general case where multiple vehicles move simultaneously across multiple lanes. We have developed several methods to calculate not only the gross weight of each vehicle but also the weight of each individual wheel. Additionally, we have created various inverse methods to deduce the individual loads applied to the structure. These methods include approaches based on mathematical models of the structure, as well as others that are agnostic to the structure's model. 1.2. Curve fitting Figure 8a illustrates this process involves adjusting a mathematical model of the structure under test to accurately match the observed time series data. When the mathematical model describes the behavior of the structure—such as how it vibrates or responds to forces—curve fitting helps refine the model to ensure it effectively reflects real-world measurements. This process enables us to more accurately estimate the variables we are interested in, such as material properties, stiffness, and damping, while also providing a clearer understanding of individual external loads acting on the structure. Initially, we estimate the variables and input them into the model, allowing it to converge toward an optimal set of values. An algorithm then optimizes these variables to ensure the function best fits the measurement data. The optimized variables represent the weight on each individual wheel.in these models a vehicle is represented as a distributed weight accounting for the weight on each individual wheel, as illustrated in Fig.8b. Fig.8d illustrates curve fitting to the time series displacement of the truck in Fig.8b traveling on the bridge in Fig.8c. 1.3 Model-Independent Approach (agnostic to the nature of the bridge): We also have approaches that do not require prior knowledge of the structure's model. in this category we learn the behavior of the structure by just observing how it responds to different "pushes" or "nudges" instead of creating a model of the bridge from its blueprint. 1.3.1. Neural Network: 1.3.1.1.Structure of the Neural Network: The network will typically have: • Input Layer: Where the network receives the input features (variables). • Hidden Layers: Where the network processes the information, typically involving multiple neurons to capture non-linear relationships. • Output Layer: Where the network provides the predicted load 1.3.1.2 Inputs channel of the neural network Let's assume that we represent the road where vehicles circulate as a two dimensional (2D) grid. In this representation, the grid consists of rows and columns, where each cell in the grid corresponds to a small section of the road. The vehicle moves through the road by occupying these cells, and their movement can be tracked as they travel from one cell to another. The grid structure (example illustrated in Fig. 9a) helps visualize the flow of vehicle and their positions at any given time, with each grid cell acting as a discrete unit that can hold a vehicle or be empty, depending on the traffic situation. Let's assume that the grid has a very high spatial resolution, such that each individual cell in the grid is small enough to distinguish between separate components of a car, including its wheels. In this scenario, instead of treating the car as a single entity occupying one grid cell, we can model the car's structure more precisely. Each wheel of the car could occupy its own cell, and the movement of the car could be tracked by the movement of each individual wheel through the grid. This approach enables a more precise representation of the car's position and motion along the road, with each wheel's location being independently updated within the high-resolution grid. In this setup, we not only track the position of the vehicle’s wheels, but also monitor each individual wheel separately, assigning a unique ID to distinguish it from the others. This allows us to determine the exact position of each wheel on the bridge, as well as its overall trajectory and path. Additionally, the system can detect when a new wheel enters the bridge and track when a wheel exits. Let’s assume that each geographical cell on the 2D grid representation of the roadways serves as an input channel to a neural network. At each instant, a specific point load corresponds to a particular wheel, representing the force the vehicle is exerting on the pavement through that wheel, which is distinguishable from others by its unique ID. Whenever a specific point load's location corresponds to a grid cell, the input channel of the neural network associated with that cell is not empty. Instead, it contains the input value corresponding to the load applied by the wheel at that specific instant. On the contrary, if at a given instant no point load is located in a specific grid cell, then the input channel of the neural network associated with that cell remains empty. 1.3.1.3 Inputs of the Neural Network The input to the neural network consists of the load (force or weight) associated with the point load applied to the specific grid cell at the input of the neural network. 1.3.1.4 Output(s) of the Neural Network The output consists of the dynamic and transient time series of an aspect of the target(s) on the structure being tested. For example in the case of bridge, we can measure the displacement of targets comprising a visual target at each time instant. For example, in the case of a bridge, the output of the neural network is the displacement of the point target(s) and for which we can also measure the motion. 1.3.1.5 Training of the Neural Network Training a neural network involves feeding data through the network, adjusting its internal parameters (known as weights—not to be confused with physical weight) based on the error between predicted and actual values, and iterating this process to minimize the error over time. In this context, weights (not to be confused with physical weight) refer to the model's internal parameters that control the strength of the connections between neurons. These weights are updated during training to improve the network’s accuracy. Initially, the network’s architecture and weights are set, and data is passed through the layers, where each layer processes the input and produces an output. The difference between the predicted output and the true target is calculated using a loss function, and this error is propagated backward through the network to compute gradients. The network then updates its weights using an optimization algorithm like gradient descent, aiming to reduce the error. This process is repeated over multiple iterations (epochs), during which the network learns to generalize from the data. Validation and testing on separate datasets ensure that the model is not overfitting and performs well on unseen data. Hyperparameters such as learning rate and batch size may also be tuned to optimize performance. 1.3.1.6 Neural Network Applications in Reverse Mode for Calculating Applied Loads on Structures By knowing the location where the point loads are applied on the structure under test at each time instance, we can identify which grid cells have a point load applied and which do not. Therefore, we can deduce which input channels of the neural network are active and which are inactive, as well as the associated output(s) corresponding to the displacement of the point target(s) on the structure under test that we measure. By knowing the active pathways and the output of the neural network, we can reverse the propagation from the output to the input layers, following the active pathways to determine the inputs at that specific moment. In practice, the number of input channels that are simultaneously activated is much lower than the total number of input channels, because vehicle traffic is limited and not all grid cells have a point load applied to them. This makes the inversion process computationally smoother. Even if we assume that, within one instance of measurement, the inverse process described above leads to an underdetermined system for determining the unknown input load, we can still solve the problem. This is because the system as a whole is overdetermined. For each individual load point, the number of independent measurements associated with that point load equals the time it takes for that point load to traverse the bridge, multiplied by the measurement rate of the displacement of the target point on that bridge. Let's suppose that the vehicle is moving at a speed of 60 miles per hour. If it takes 4 seconds to traverse the bridge, that means the bridge has a length of 352 feet, which is relatively small. Having 240 point loads on that bridge simultaneously is highly unreasonable. Therefore, the total number of independent measurements we make for each point load far exceeds the number of point loads on the bridge (the unknowns). The system is overdetermined, as the number of independent measurements (known values) exceeds the number of unknown point loads. Side note: Keep in mind that, in addition to detecting different vehicles in each traffic image frame, we have also trained a custom object detection model specifically for identifying vehicle wheels. Furthermore, we use an object tracking algorithm that associates and tracks each vehicle and associated point loads across time, linking point-loads from one frame to the next, with each point-load being assigned a unique ID. We create a grid-like representation of the bridge, where each grid point corresponds to the intensity of a point load applied at that location. These grid points serve as the inputs of a neural network. The output is the target(s) displacement. During the training process, the parameters of the neural network (weights and biases) are optimized. During operation, to determine individual load applied at the inputs, we backpropagate the output through established flow paths, leveraging our knowledge of activated inputs to identify the utilized paths, as we can determine which inputs are activated at each moment 1.3.2 Impulse Response Approach to Determine Individual Applied Loads At each measurement point, the output is the result of combining the displacements caused by individual forces applied at various locations on the bridge. This formula treats each instance where the vehicle makes contact with the pavement as separate point loads. ^^^^ = 1, ... , ^^^^ is an index for each of the N point force on the bridge at time k.^^^^^^^^, ^^^^^^^^ is the to-be-determined weight of each point load on the bridge, and ℎ(^^^^^^^^,^^^^^^^^) is the modelled bridge deflection expected for a unit ^^^^^^^^ℎweight located at position (^^^^^^^^,^^^^^^^^). The known are ^^^^^^^^(the time-series displacement measurement), and across the bridge the unknown are the W( )the weight of individual point. Since the number of independent equations exceeds the number of unknowns, this is an atypical inverse problem that is overdetermined, and we can determine the unknowns. In the long run, we believe that adopting a neural network approach will be more robust and reliable. However, for the time being and for demonstration purposes, our approach will involve implementing an impulse method. 1.3.2.1 Mathematical Description of the Impulse Response Implementation In this approach, we represent the bridge as a two dimensional (2D) mesh, irrespective of the bridge e's type each node’s x and y coordinates identifying specific locations of a point load (vehicle’s wheel) on the bridge. For instance, the picture in Figure 9A illustrates a scenario with four distinct load points, labeled A, B, C, and D, each positioned at different locations within the measurement at a given instance.

[0002] Fig.9B shows the displacement of the visual target that is measure is the combination of the displacement induced by each single load on the bridge as described by: Since we know the location of the load points at each instance and can track them across consecutive measurements, we are able to implement the equation mentioned above. Having established the equation so far, we will now transition to a global matrix description to provide a comprehensive overview of the problem, which can also be easily implemented as a computer algorithm. Given an ^^^^ × ^^^^ mesh grid representation of the bridge, for each grid position^^^^there a coefficient ℎ^^^^,^^^^that relate the displacement of the target on the to the load applied to the bridge at grid position�^^^^^^^^,^^^^^^^^�, ù ú ú úThe first step is to flatten the ^^^^ × ^^^^ 2D ^^^^ matrix into a 1D vector vec(H) oflength ^^^^ × ^^^^ Let’s use the same example we considered earlier, where there are point loads Wa, Wb, Wc, Waapplied at different locations. These point loads represent the total load on the table during a specific measurement interval, say between time t=1and t=N ^^^^^^^^^^^^ =�^^^^^^^^^^^^^^^^� ^^^^^^^^Let’s represent all these elements as a column vector. As a case study, let’s consider the following example to illustrate how the problem is addressed. At time t=1 Wc, Wdare applied on the bridge then^^^^^^^^=1 = 0.^^^^^^^^ + 0.^^^^^^^^ + ℎ9.^^^^^^^^ + ℎ78.^^^^^^^^At time t=1 WbWc, Wdare applied on the bridge^^^^^^^^=2 = 0.^^^^^^^^ + ℎ2..^^^^^^^^ + ℎ15.^^^^^^^^ + ℎ90.^^^^^^^^then ……………………………………………………………… ……………………………………………………………………….. ……………………………………………………………….. At time t=N Wa ,Wb,Wc, Waare applied on the^^^^^^^^=^^^^ = ℎ5.^^^^^^^^ + ℎ98.^^^^^^^^ + ℎ8.^^^^^^^^ + ℎ9.^^^^bridge, then^^^^Now we aggregate the outputs into a column vector ^^^^ ^^^^^^^^^ù ú ú ú ^^^^^^ûlocation of ^^^^^^^^at time t=N By using matrix representation, we can separate the known variables from the unknown variables. On one side is the displacement of the point target on the structure D, where each component corresponds to a time instance measurement. There is a row matrix W, where each component corresponds to a specific load, identified by its unique ID, applied to the structure during the time span described here, which is a subset of the total measurement period. Matrix A is generated based on traffic analysis. For each load in question, if the specific load was present on the structure at the time of measurement, it is multiplied by the impulse response coefficient corresponding to the location where the load was applied to. Matrix created based on analysis of traffic feed data This matrix is also a known parameter of the problem. knowns of t We can rewrite the equation slightly differently by keeping the dimensions of matrix A constant. To ensure compatibility for operations, we would adjust the dimensions of W by adding zero-padding, making it compatible with A. Applying matrix algebra we estimate the point loads, ^^^^ = ^^^^.^^^^^^^^^^^^^^^^ = ^^^^^^^^^^^^. ^^^^^^^^^^^^^^^^ = ^^^^^^^^^^^^. ^^^^^^^^^^^^^^^^ = ^^^^−^^^^^^^^−^^^^^^^^^^^^^^^^ ^^^^Therefor we can estimate the point loads (^^^^^^^^^^^^)−^^^^^^^^^^^^^^^^ = ^^^^Additional example Matrix D: The matrix D contains the displacement measurements of point target(s) on the structure under test at each time instance. Matrix W Let ^^^^ be a vector matrix where ^^^^1, ^^^^2,.., ^^^^^^^^,.., ^^^^^^^^represent distinguishable loads applied at various grid locations over the time segment under consideration Matrix A: The matrix A captures the spatial-temporal values associated with each load applied during this experimental segment. 1. Let ^^^^1, ^^^^2,.., ^^^^^^^^,.., ^^^^^^^^represent multiple loads applied at various grid locations over the time segment under consideration. 2. Each load ^^^^^^^^ is applied at a grid location (^^^^^^^^(^^^^), ^^^^^^^^(^^^^)) that may vary withtime t. 3. ℎ(^^^^^^^^(^^^^), ^^^^^^^^(^^^^)) is the impulse response associated with the grid location(^^^^^^^^(^^^^), ^^^^^^^^(^^^^))4. Then, the matrix A can be defined as follows: )^^^^^^^^,^^^^represents the value in row t (time step) and column s (specific load) in matrix A. ─This matrix A provides a temporal snapshot for each load ^^^^^^^^applied at a possibly varying grid location over time, capturing the spatial-temporal values associated with each load throughout the experiment segment. ─ We can significantly improve the efficiency and speed of the computation by adopting a segmented time approach, where matrix A is updated to focus solely on the current time segment. Previous loads are discarded once they have been determined, and any new loads that arise in subsequent segments are incorporated as needed. Here’s one approach that could work, though other alternatives may also be possible : 1. Define Time Segments: The experiment is divided into consecutive time segments: oFor instance, from t0 to t2, then from t1 to t3 , and so on such ^^^^0 ≤^^^^1 ≤ ^^^^2 ≤ ^^^^32. Matrix A within Each Segment: For each time segment: o Matrix A captures only the loads that are active within that specific segment. o Any loads that are fully determined in a previous segment are removed from A when moving to the next segment. o New loads that arise in the current segment are added to A. 3. Continuous Updating and Dropping of Loads: o As time progresses from one segment to the next, previous loads that have been fully determined are removed from A, reducing the matrix’s complexity. o New, undetermined loads are added as they appear, ensuring that A remains focused on the loads currently under analysis. 4. Synchronize with Other Matrices: o Matrices D and W (representing displacements and loads, respectively) are updated in tandem with A to reflect only the active loads for each segment. o This keeps all matrices aligned with the specific load conditions of the current time segment. Example Workflow: • For the time segment t0 to t2: o Matrix A includes loads applied within t0 to t2 and determines their impact. • Moving to the next time segment t1 to t3: o A drops the fully determined loads from the t0-t1 segment and adds any new loads active in the t1-t2 segment. o Matrices D and W are similarly updated to reflect the new load conditions. Benefits: This segmented, adaptive updating of A, D, and W achieves: • Computational efficiency by discarding loads that no longer need processing. • Adaptability by focusing resources on newly applied loads, optimizing the analysis of current conditions without the burden of obsolete data. This approach allows the experiment to proceed in manageable segments, efficiently processing each load without needing to store or compute irrelevant historical data. 1.4 Calibration Using the same approach, with D and W known and A as the variable to be determined, we can calibrate the system As an example, in the previous equation, where ^^^^ is expressed as a function of ^^^^ and ^^^^, we can deduce the non-zero elements of ^^^^. Since we know the location of the point loads at each instant, we can use this information to identify the corresponding elements in ^^^^ that contribute to the system's response. This allows us to recover the impulse response at the points where a point load has been applied. In our case, system calibration consists of performing system identification thatconsists of determining each element ℎ(^^^^, ^^^^) in the system's 2D impulse response overa mesh representation of the road. Here, each ℎ(^^^^, ^^^^) represents the system's response ata specific point (^^^^, ^^^^) on the road mesh when an impulse is applied at that location. Byidentifying each ℎ(^^^^, ^^^^) we map out the system's complete spatial response, capturinghow an impulse at each point on the road mesh influences the output. To conduct system identification, we have two main approaches. The first approach uses algorithms based on deconvolution, where the goal is to reverse the convolution process. In this method, the system's impulse response is recovered by using known inputs and their corresponding outputs. The objective is to determine the impulse response by "undoing" the convolution between the input and the system. Essentially, this approach aims to identify the system’s characteristics that would have produced the observed output from the given input. There are several deconvolution techniques used in various fields, each suited to different types of data and problems that can be modified and tailored for our specific application. Examples include standard deconvolution, which reverses the convolution process when both input and output are known; blind deconvolution, where the input is unknown, and both the input and the system's impulse response must be estimated simultaneously; Lucy-Richardson deconvolution, an iterative method commonly used in imaging; Wiener deconvolution, which minimizes mean square error and works well in noisy environments; Tikhonov regularization, which stabilizes deconvolution by adding a regularization term to prevent overfitting; and Fourier domain deconvolution, which operates in the frequency domain for linear systems. These methods, along with others such as maximum entropy and least squares deconvolution, represent a wide range of approaches available for solving deconvolution problems across various applications. The methods outlined above are just examples of the deconvolution techniques that could be adapted to our problem of determining the 2D spatial impulse response matrix, given known input and output data. Depending on the characteristics of the system and the available data, other deconvolution methods may also be suitable. These could include alternative iterative approaches, more advanced regularization techniques, or specialized algorithms designed to handle noise, non-linearity, or other complexities in the system. The choice of method will depend on factors such as the quality of the input and output data, the system's response, and computational resources available. 1.4.1 Determining Impulse Response Without Knowledge of Input (Unknown Vehicle Weight) In blind deconvolution, where the input is unknown, only the output is available. In this case, the goal is to simultaneously estimate both the system’s impulse response and the input. This method assumes that there is enough information in the observed output to infer both the impulse response and the input, often relying on additional constraints or assumptions about the system's behavior. We can identify a system's impulse response using sparse inputs but without knowing their exact intensities using: • In one case, we know exactly where the point loads are applied at each instant and have access to the output, which represents sparse excitation, as only a limited set of locations in the 2D space experience forces at any given time. We then use blind deconvolution to estimate the intensity of these forces, as the same point load can be applied at various locations across the 2D impulse response multiple times. • In the context of 2D spatial impulse response estimation with sparse excitation, blind deconvolution works by leveraging the fact that inputs (such as impulses or point loads) are applied sparsely at specific, known locations and times, but the values of these inputs are unknown. Sparse excitation refers to the situation where inputs occur only at a limited number of points in time and space, and the rest of the space and time remains unexcited (i.e., no input is applied). Here's how blind deconvolution works in this case: o Known Information: We know the output of the system at each spatial point and time, as well as the locations and times at which the inputs are applied, but we do not know the actual values of these inputs. The key assumption in sparse excitation is that inputs are rare or occur at only a few points in time and space, making the input signal sparse. o System Model: The system’s response at each spatial location and time is governed by the convolution of the unknown input signal with the 2D impulse response of the system. The observed output at each point in space is the result of the system’s impulse response interacting with the sparse inputs. o Blind Deconvolution Goal: The goal is to recover the impulse response of the system and the unknown input values at the locations where the inputs were applied, given only the output data and the knowledge of when and where the inputs were applied. This means that we aim to estimate both the system’s characteristics (the impulse response) and the missing input values at the sparse locations. o Iterative Process with Sparse Constraints: Since the input is sparse, the deconvolution algorithm can use this sparsity as a constraint. It starts with an initial guess for the impulse response and input values, then uses the locations and times of the inputs to refine these estimates. The sparse nature of the excitation helps the algorithm focus on estimating the values of the input only at the specific points where inputs were applied, rather than inferring the entire input signal. o Optimization: The process typically involves iterative optimization, where the input values and impulse response are adjusted to minimize the error between the predicted output (based on the convolution of the estimated input and impulse response) and the observed output. The sparsity constraint ensures that the input values are non-zero only at the known locations where inputs were applied, reducing the complexity of the problem and making the solution more tractable. o Result: After several iterations, the algorithm converges to an estimate of both the impulse response and the sparse input values. The estimated impulse response describes how the system reacts to inputs at different spatial locations, while the estimated input values correspond to the locations where the excitation was applied. In summary, blind deconvolution with sparse excitation takes advantage of the fact that inputs are applied at specific, sparse locations, and uses this sparsity to efficiently estimate both the system's impulse response and the values of the unknown inputs. The sparsity constraint significantly reduces the complexity of the problem, making it feasible to recover both the system's characteristics and the input signal. 1.5 Architecture of Computer Code for Implementing an Impulse Response Approach 1.5.1 The goal The objective is to automatically generate a dynamic table that, for each measurement instant, identifies the applied point loads, their respective locations, and the measured displacement of the target. The table is dynamic and automatically updates with each measurement. With these table values, we can easily perform the matrix arithmetic from the previous section. This configuration organizes data by time tags, where each time tag (e.g., "time_tag1") contains an array of point loads, each with a unique pointloadID, followed by the corresponding XpointloadIDand YpointloadIDcoordinates, and at the end, the position or displacement of the visual target on the bridge, represented by its own X and Y coordinates.

[0003] 1.5.2 Challenges Several challenges exist, but we have solutions for all of them: 1. The data collection from traffic is not aligned with that of the bridge displacement because the recording is handled separately. Since we have one stream of data collected for traffic and another for displacement, these data streams may be slightly offset due to differences in their collection time instances. The Solution: Both data streams are synchronized using a common time reference, such as Universal Time Coordinated (UTC) or GPS time, though other synchronization methods may also be used. To align the streams, we can compare their respective time tags and match those that are closest to each other. 2. Not all wheels of a vehicle traversing the bridge are always simultaneously within one single camera's field of view. Solution: There are multiple approaches: Creating a comprehensive visualization (stereovision) of the entire road traffic using multiple cameras. Utilizing multiple cameras enables the construction of a comprehensive and detailed 3D visualization of the scenery, precisely capturing depth, texture, and spatial relationships. In another embodiment, incorporating various types of sensors—such as LiDAR, stereo cameras, and time-of-flight sensors—further enhances the accuracy of the 3D representation by integrating diverse perspectives and depth information. Single Camera However, by using just a single traffic camera, we can still extract the necessary information from all the vehicles moving on the road. As explained below, this approach overcomes the limitation of a single camera where depending on the location of a vehicle on the road relative to the camera's field of view, a single camera may only capture a portion of the vehicle, meaning not all of its wheels can be seen at all times. The user selects a Region of Interest (ROI) within the video feed of the traffic. The limitations of using a single camera are that ,depending on a vehicle's position on the road relative to the camera's field of view, the camera may only capture a portion of the vehicle, meaning that not all of its wheels are visible at all times. However, by carefully selecting Regions of Interest (ROIs) within the camera's field of view in such a way that as a vehicle enters these areas, the camera can clearly capture the vehicle's axles, allowing them to be differentiated. Within the ROI illustrated in Figure 10 and 11, the axles of any vehicle present are visible. Our tracking algorithm can then detect if a vehicle's position is within one of the ROIs, and as the vehicle enters, the algorithm extracts an image of the vehicle.─ and this is possible because we have a vehicle object detection and tracking algorithm that is continuously applied to the traffic video feed. Using a custom-made object detection neural network, which we specifically trained to identify wheels alongside other objects within a larger image, we can determine the position of the wheels within the image of the specific vehicle. To understand spatial relationships and distances in the image, we calibrate using reference points within the ROI with known spatial relationships. This is straightforward because freeway features are similar and their distances are consistently predictable ─also, by using a range finder, we can quickly measure the distance between the camera and any of these features, thereby realizing a quick in-the-field calibration of our tracking system. However, in practice, especially on wide roadways with multiple lanes and dense traffic, each time we extract the image of a vehicle by cropping the segment of the image allocated and selected as the vehicle from the traffic feed, some segments of other vehicles may still be visible, along with wheels not associated with the vehicle. Similarly, when detecting the number of axles, not all wheels of the vehicle are relevant to the analysis. Detecting wheels that are not relevant to the axle analysis can lead to errors, unless we can differentiate the wheels of interest from the others. To achieve this, we have developed an algorithm that selects the relevant wheels for analysis by considering the constraints of the problem. The number of axles of the vehicle with wheels on the road, among all the wheels for which we detect the center location in the image, corresponds to the maximum number of collinear points with a slope equal to the direction of the vehicle's movement, within some allowable error. We can also improve the algorithm by adding additional constraints to the problem. As the vehicle enters the ROI, its image is extracted from the video feed. From that image, we identify the vehicle's axles and deduce the relative distances between the wheels of the vehicle. To achieve this, we have developed a custom neural network trained to detect images of wheels alongside other objects within a larger image. By extracting the image of the wheel, we can classify them based on different characteristics, with the classification depending on the specific requirements. To understand spatial relationships and distances in the image, we calibrate using reference points within the ROI with known spatial relationships. This is straightforward because freeway features are similar and their distances are consistently predictable. Also, by using a range finder, we can quickly measure the distance between the camera and any of these features, thereby realizing a quick in- the-field calibration of our tracking system. As a vehicle moves across the bridge, we track its trajectory. Once it has finished traversing, we can determine the trajectory of each individual wheel from the vehicle's trajectory, since the relative position and distance of each wheel on the vehicle remain constant. 3D mapping of object locations from 2D images: There are various methods for accomplishing this such as, but not limited to o Monocular Depth Estimation: Uses a single image and deep learning models to predict depth at each pixel. Quick but less precise. o Stereo Vision: Uses two cameras to compute depth based on disparity (difference in position of an object between the two images) and triangulation. Accurate but requires two synchronized cameras. o Structure from Motion (SfM): Utilizes multiple images from different angles, matching features across images and applying triangulation and bundle adjustment to reconstruct 3D geometry. Accurate but computationally intensive. o Deep Learning 3D Reconstruction: Employs neural networks to create 3D models (e.g., point clouds, voxels) from single or few images by learning depth cues and shape patterns in the data. Versatile but data-intensive. o Depth Sensors: Active sensors (LIDAR, RGB-D) measure accurate distances using time-of-flight or structured light techniques, often combined with RGB images for detailed 3D maps. Accurate but requires additional hardware. o Single-Image 3D Reconstruction Using Known Reference Points: Uses perspective geometry and homography transformations to map 2D image points to 3D space when the physical dimensions and positions of certain points are known. This approach leverages properties like camera intrinsic parameters, vanishing points, and reference scaling to calculate 3D positions relative to the camera. Each method relies on different mathematical principles, from disparity and triangulation to perspective transformations, with the reference-point method being effective when specific real-world size and location information is available 1.5.3 Computer system architecture Figure 12 illustrates our software architecture is based on three different main programs that operate simultaneously. Program 1 processes traffic data, while Program 2 manages bridge deflection analysis. Both programs will automatically and continuously send output data to a third program, which will associate the data from Programs 1 and 2 based on their time tags, align them, and perform the necessary arithmetic calculations to infer the final output results. 1.5.4 Program1 Architecture Initialization Step (illustrated in Figure 13): The user specifies information via a Graphic User Interface: o Selecting the Region Of Interest (ROI) on the Traffic Video Feed: The user must choose the ROI to ensure that a vehicle inside the ROI is positioned so that all its axles are visible in the image. When the vehicle enters this area, its image is captured to analyze its features. Alternatively, the selection of the ROI can be done automatically by using an algorithm that automatically determines the position of the camera relative to the road by detecting specific features that are characteristic of roads o Selecting Reference Points on the Video Image: The user selects reference points on the video image and provides information about their relative distances. This data is used to transform the 2D image of the field of view into a realistic spatial representation. Using that transformation, at each measurement instance when we detect the location of an object within the camera frame, we can deduce its 3D location on the road Main program The program detects vehicle, tracks their trajectory across the bridge, and assigns a unique ID (e.g., 183, 179) to each one, as illustrated in Figure 14a. The system then starts logging the location of the detected vehicle in an initial log table structured as a dictionary where each time tag is linked to a set of information, “trajectory_by_time_defautdict”. In one nonlimiting embodiment, the disclosed method enables the reduction of traffic cameras to as few as a single camera, while still accurately tracking and identifying the trajectory of individual vehicle components, such as wheels, by leveraging advanced trajectory analysis as explained herein. As a vehicle enters the ROI, information about the vehicle, such as its wheels emplacements, number of axles, approximate vehicle size, plate and DOT numbers, is extracted. (The region of interest (ROI) should be selected such that the camera's position allows for the recognition of the different axles of the vehicle, We can also have multiple regions of interest (ROIs); for example, one ROI for each lane, or two types of ROIs: one for detecting vertical information about the vehicle, such as axle separation and Dot number, and another for capturing horizontal information, such as vehicle width or license plate number.) This allows for identifying the exact position of each individual wheel on a car in relation to the others. By tracking each car's trajectory, we can reconstruct the path of each individual wheel and assign a unique ID to each one, without requiring each side of the vehicle to remain within the camera's field of view for the entire traversal. The information extraction could be managed by a separate thread to avoid slowing down the main program. However, in practice, when we extract the image of a vehicle entering the region of interest, it’s possible for parts of other vehicles to appear in the frame as well. Additionally, simply implementing our custom-made neural network that detect wheels does not necessarily ensure that we correctly identify the axle of the intended vehicle. This could lead to errors in estimating for each vehicle the number of axles and their spacing, as shown in Figure 14A. We successfully developed an algorithm specifically for this purpose, and it has proven reliable in real-world testing so far. When multiple wheels are detected, using this algorithm the system automatically identify the relevant ones for this analysis and differentiate them from the rest. As shown in the attached screenshot of my computer, four wheels are detected, but only two of them are relevant for the axle separation calculation. This software relies on vector direction and collinearity. To achieve this, we have developed an algorithm that selects the relevant wheels for analysis by considering the constraints of the problem. The number of axles of the vehicle with wheels on the road, among all the wheels for which we detect the center location in the image, corresponds to the maximum number of collinear points with a slope equal to the direction of the vehicle's movement, within some allowable error. We can also improve the algorithm by adding additional constraints to the problem. We have two log tables that are globally readable and writable by all functions within the program. trajectory_by_time_defautdict: includes only location information about the vehicles at each instant, without differentiating its wheels. reshuffle trajectory_by_time: This uses the information already captured in “trajectory_by_time_defautdict” to assign a unique ID to each wheel within a vehicle based on the information extracted about the vehicle upon entering the ROI. For instance, If a vehicle has an ID named VehicleId and contains 4 wheels, the program will generate unique IDs for each wheel, such as VehicleId_1, VehicleId_2, VehicleId_3, and VehicleId_4, instead of using VehicleId alone. Additionally, since we are tracking the motion of each individual vehicle during the traversal, we can deduce the trajectory of each wheel, as we know the relative position of each wheel on the vehicle, which remains fixed. To prevent slowing down the main program, operations related to this logging table—such as using the location of vehicles to deduce the location of their wheels at each instant—can handled by an independent thread

[0004] In summary, as a vehicle enters the field of view of the traffic camera, a unique ID is assigned to it, and its trajectory is tracked across the frame until it exits the bridge. During this traversal, as the vehicle enters the ROI, we extract information about its size, axle separation, axle numbers, and deduce the relative position of its wheels along its plate number DOT number, and conduct different types of vehicle classification, such as, but not limited to, vehicle type, model, and color and etc. ─Additionally, by using acoustic sensors, we can apply an acoustic signature to each individual vehicle, including frequency and intensity patterns, as well as detect if the noise associated with the vehicle exceeds or falls below the allowed threshold- Leveraging this knowledge, we can reconstruct a new table that contains information about the location and unique ID of each individual wheel at every time instance, along with the various characteristics of each vehicle. This information can be sent gradually to a third-party program as each vehicle exits the table, without slowing down the main program, by using parallel threads and sockets, for example. 1.5.5 Program2 Architecture In the case we use camera to measure the displacement time series of target (s) on the structure(as an example a bridge) For each measurement, we have the X and Y coordinates of the targets relative to the camera's frame of reference, other relevant information and metrics for that measurement instance, a time tag. Also, X and Y could represent the 2D coordinates of the object in the camera's frame of reference, relative to an inertial reference frame. This means that X and Y are the coordinates of the object as observed by the camera, considering the camera's perspective, and these coordinates are measured relative to a fixed, inertial reference frame. In other words, X and Y are the coordinates in the camera's view, but are referenced to a stable, global coordinate system (the inertial frame), which might be used to track the object's position in space. We can also measure the displacement of the target where x and y are the current coordinates of the target, and x1 and y1 are the coordinates at an earlier time, the change in position can be calculated by subtracting the earlier coordinates from the current coordinates. Here's the general formula for the displacement or change in position: o Change in x coordinate Δx=x−x1 o Change in y coordinate Δy=y−y1 Where: • x and y are the current coordinates (at the later time), • x1 and y1 are the earlier coordinates (at an earlier time) o In another context, x1 and y1 could represent the average values of the coordinates over a certain interval of time. o In another context, x1 and y1 could represent the average values of the coordinates over a certain interval of time that is changing over time. 1.5.6 Program3 Architecture The Program3 continuously receives information as sockets from both Program1 and Program2, as illustrated in figure 14b. o The primary function is to link or pair information from Program1 with data from Program2 by matching their timestamps. It finds and associates the data from each program that has the closest timestamps. o It performs the mathematical operations outlined in sections 1.3.2.1 and 1.4 above. 3. Determining Static Values and Dynamics of Individual Point Loads Let’s revisit the example where a vehicle is traveling at 60 miles per hour and takes four seconds to cross a bridge. During this time, data is collected at a rate of 60 points per second, yielding 240 data points of point load versus time. Fig.14c illustrates in the case of a vehicle, a point load model of the force that a vehicle’s wheel-suspension system applies to the structure under test. Wheel-suspension system dynamics involve both static and dynamic forces acting between the wheel, suspension components, and the road. The static force is the constant downward force from the vehicle's weight on the pavement, ensuring steady tire contact. In contrast, dynamic forces stem from vehicle motion, road irregularities, bridge dynamics, and suspension movement, influencing handling, shock absorption, and stability as the vehicle adjusts to varying road conditions. By analyzing the dynamics of each point load and considering the multiple wheels on each vehicle—where each point load represents an individual wheel- suspension system—we can gain an unprecedented, comprehensive understanding of the vehicle suspension system's performance, even without direct access to it. From this time-based data set, we can determine the static force by calculating the average. By further analyzing the oscillations, we can identify both the dynamic behavior of the suspension associated with the point load and, separately, the bridge dynamics. 4. Characterizing Vehicle Suspension Performance Without Access to the Vehicle By analyzing the dynamics of each point load and considering the multiple wheels on each vehicle—where each point load represents an individual wheel- suspension system—we can gain an unprecedented, comprehensive understanding of the vehicle suspension system's performance, even without direct access to it. 5. Improve spatial resolution In this case, we use a camera to make our measurements by measuring the displacement of objects within the camera's frame. In this approach, we generally utilize the image sensor of the camera as our measurement device, extracting the data to an external unit to implement our own image capture pipeline (To prevent unintended image compression by the camera's internal processes). Additionally, we developed our own measurement algorithm, which we implement on a GPU for real-time processing. To enhance spatial resolution, we enlarge the image while mitigating any deterioration in quality utilizing a computing system that calculates time series displacement of visual target(s) that employs Super-Resolution Convolutional Neural Networks (SRCNNs) to improve the spatial resolution of images through advanced algorithmic super-resolution techniques to increase the spatial resolution of the measurement. ─This approach contrasts with conventional digital zooming methods that use linear interpolation. Linear interpolation estimates new pixel values by averaging neighboring pixels, which can degrade image quality. This degradation happens because pixels are digitally enlarged to fill gaps, rather than optically adjusting the lens, which maintains better image fidelity. Super-Resolution Convolutional Neural Networks (SRCNNs) enhance spatial resolution by intelligently increasing pixel density and adding fine details to low- resolution images. First, the SRCNN up samples the image, typically through interpolation, to a higher resolution. Then, it uses convolutional layers to extract essential features, such as edges and textures, from the upscaled image. These features are processed through a non-linear mapping layer that learns to translate low- resolution patterns into detailed high-resolution equivalents based on its training data. Finally, a reconstruction layer combines these enhanced features into a smooth, high- resolution image. Through this layered approach, SRCNNs effectively add realistic details and clarity that are not achievable with simple upscaling methods, producing images that appear sharper and more detailed. 6. Gross Weight By calculating the integral of the displacement time series caused by a vehicle as it traverses a bridge, insights about the vehicle gross weight could be obtained. For the sake of simplicity, let's consider a single-lane traversed by a single truck. Let’s consider the graph of the time-series deflection, d(t) of the visual target during the truck’s passage. Let’s call u(t), the impulse response, i.e., the deflection that a point load of mass unity cause to the bridge when traversing at a nominal speed V0. u(t) is compressed or stretched along the time axis as the point load moves faster or slower. To characterize this scaling, we introduce a variable, v / v0, where v represents vehicle speed, and v0an nominal speed. Thus, we can write our impulse response function as: �. A point load of weight Pi, moving at a speed of v, produces the following time-series deflection on the bridge: �, ^0To complete our model, we can introduce a delay, ti, to identify the time when the point load starts traversing the bridge. ^^^^ − ^^^^^^^^^^^^(^^^^, ^^^^) = ^^^^ ^^^^^^^^ .^^^^� ^^^^� �^^^^0Assume that the first axle crossed the bridge at time zero, then ^^^^^^^^ ^^^^ where di, is the spacing between the point load Piand the first point load. we can derive the following equation: (^^^^) Integral: The area representing the integral of the time series deflection, S, can be easily calculated. This leads to: We can make two assumptions: • For the same vehicle, we assume, ^^^^ to be the same for all axle weight. That means that all axles of the vehicle have the same bridge’s crossing time. • We start by approaching the problem by neglecting the mutual overlapof the ^^^^�^^^^−^^^^^^^^^^^^� ^^^^� with each other. This is true when every axel tandem is treated as a 0 single point load, and each point load is sufficiently separated from the other. These two assumptions lead to: .^^^^^^^^ S, the integral area of the time-series deflection, can be easily computed. Also, A is related to , which is known, by a scaling factor that depends on ^^^^ / ^^^^0; that is ^^^^0 7. Health monitoring Fig.14d illustrates we have a system that simultaneously integrates several independent features, including measuring bridge dynamics and transients, traffic patterns, and the determination of external loads applied to the structure. This integrated and data fusion system measuring bridge dynamics, traffic load, and load analysis offers a highly integrated approach to monitoring and managing bridge health. In the case that the target structure is a bridge, the real-time measurement of bridge dynamics, traffic load, and load analysis offers a highly integrated approach to monitoring and managing bridge health. Traffic data and load analysis together determine the types and magnitudes of forces exerted on the bridge and provide insight into how these forces affect the structure's overall stability. Simultaneously, dynamic monitoring tracks the bridge’s physical response—such as vibrations, stress, strain, displacements and deflections—to these applied loads. The interaction between these three measurements provides a clearer picture of the bridge's performance, where changes in traffic flow or load stress can be directly correlated with structural behavior. This allows for more accurate predictions of wear or damage, supports more effective maintenance planning, and improves overall safety and efficiency by addressing issues before they become critical. At the same time, it enables the continuous calibration of the system to solve the inverse problem of detecting individual loads from the dynamics of the bridges. The present invention relates to methods for structural health monitoring (SHM) that focus on detecting changes in the behavior and performance of structures over time, rather than measuring absolute values. These methods involve identifying variations in structural parameters, which are critical for assessing the health and integrity of the structure. For example, using the displacement time series of targets on a structure, we monitor changes in its structural characteristics and behavior. We perform both temporal and Fourier analyses, as well as Laplace analyses. By analyzing the power spectral density of the time series, we can detect the natural resonances of the structures, including their associated linewidth and peak. This information, along with many other insights, guides us in understanding and restoring the structural condition. Applying these analyses enables us to glean valuable information regarding the structure's behavior, performance, and response to various influences. This capability facilitates effective monitoring, allowing for the identification of variations even in the absence of reference modes, among other applications. Fig 15 illustrates an example where we have been recording the time series displacement of a bridge in real-time at a rate of 60 frames per second, using an ultra- high-resolution optical camera and developing our own image processing unit and tracking algorithm. ─This also illustrates the sensitivity of our measurement system to detect even the impact of individual wheels on overall displacement measurement─. By calculating the power spectrum density of the time series (as illustrated in Figure 16), we can identify the resonance mode frequencies of the structure, along with the linewidth associated with each mode Monitoring Changes in: • Resonance Frequency Tracks shifts in the natural vibration frequency of the structure, which can indicate changes in mass or stiffness. • Resonance Linewidth Observes the width of the resonance peak in the power spectrum, providing insights into energy dissipation and potential structural damping changes. • Stiffness Monitors changes in the structure's resistance to deformation, where a reduction could signal damage or weakening • Phase in time series data A phase shift in the time series data is a strong indicator of a sudden structural change, such as a connection becoming loose or broken, which could signal potential damage or instability in the structure. There are several methods for detecting phase shifts in time series data, each with its unique strengths and applications. The cross-correlation method compares two time series by calculating their similarity as a function of time-lag, allowing for the identification of the lag where correlation is maximized, which indicates the phase shift; this approach is particularly effective for periodic signals. The Fourier Transform method utilizes the Fast Fourier Transform (FFT) to convert time series data into the frequency domain, enabling the comparison of phase angles at dominant frequencies between two signals to detect shifts, making it ideal for analyzing signals with periodic components. The peak detection method identifies peaks in both the reference and shifted signals, with the time difference between corresponding peaks serving as a direct measure of the phase shift; this method is intuitive and particularly suited for cyclical data with well-defined peaks. Finally, the wavelet transform method applies a wavelet transform to capture phase shifts across different scales and time points, making it highly effective for non-stationary signals that exhibit varying frequency components over time. Each method provides valuable insights depending on the nature of the time series data and the specific application. As an example, a method for detecting changes in the resonance frequencies of a structure comprises calculating the power spectral density of time series deflection data and observing variations in the resonance frequencies. As another method, the linewidth of a resonance peak in a structure is indeed related to how energy is stored and dissipated. Changes in this linewidth indicate variations in energy dissipation. In the case that the target structure is a bridge, energy damping in a bridge occurs through its supports and foundations by mechanisms such as material damping in bearings, frictional losses, soil-structure interaction, and load redistribution. Understanding these processes is crucial for evaluating a bridge's performance and ensuring its safety and longevity under various loading conditions. The linewidth of a resonance mode of the structure, which relates to energy dissipation, can provide valuable information about the interaction between the structure and its surrounding environment. Changes in the linewidth can indicate alterations in the mechanical properties and characteristics of the surrounding environment. As another example, we can monitor changes in the stiffness of the bridge by detecting variations in the average intensity of deflection caused by the passage of similar or known vehicles. The stiffness of a bridge is the relationship between the applied load and the deflection it causes. Alternatively, a statistical approach can be employed, where we take the average deflection over an extended period while simultaneously utilizing traffic data to determine the number and types of vehicles traversing the bridge at any given time. This combined analysis allows for a more accurate assessment of stiffness changes. As another option, the method involves analyzing correlations in different segments of time series deflection data to detect changes in stiffness over time. A sliding window approach can be used to monitor changes in bridge stiffness by analyzing segments of time series deflection data. By moving the window across the data, you can track how deflection changes over time in response to similar or known vehicle loads. Correlating deflection patterns between windows helps identify whether stiffness is stable or decreasing. By using traffic data, you ensure that deflections are compared for vehicles of similar types, avoiding inconsistencies due to varying loads. A statistical approach can be employed, taking the average deflection in each window and monitoring significant deviations over time. If deflections increase under similar loading conditions, it may indicate a reduction in stiffness, signaling potential structural issues or deterioration. The correlation analysis between consecutive windows allows for a more accurate and continuous assessment of the bridge's structural health. 7.1 Distinguishing Changes in Measurements Due to Ambient Environment Variations As demonstrated, we have a structural health monitoring approach that focuses on detecting changes in key characteristics related to the structural properties of the target structure, made possible by the nature of our measurements. However, for this approach to be reliable, we must differentiate changes caused by the ambient environment from those resulting from structural changes. To distinguish changes in those parameters resulting from actual structural alterations from those induced by fluctuations in environmental conditions, we deploy along with our measurement apparatus and automated whether stations. The automated weather station equipped with sensors to measure various meteorological parameters such as temperature, humidity, wind speed and direction, atmospheric pressure, and precipitation, it is capable of autonomously collecting and transmitting this data, eliminating the need for human involvement in the data collection process. We can effectively correlate changes in environmental conditions with changes in our measurements and discern the contributions of environmental factors versus other sources to the observed variations by employing multiple methods. Some of these methods include: Correlation Analysis: This involves assessing the degree of association between changes in environmental variables (such as temperature, humidity, etc.) and changes in our measurements. Statistical measures like Pearson correlation coefficient can quantify the strength and direction of this relationship. Multiple Regression Analysis: In this method, we analyze how multiple environmental variables collectively influence our measurements. By including various environmental factors as independent variables in a regression model, we can estimate their individual contributions to the changes observed in our measurements while controlling for other factors. Time Series Analysis: Time series techniques can be used to analyze how changes in environmental conditions over time correspond to changes in our measurements. Methods like autoregressive integrated moving average (ARIMA) modeling or seasonal decomposition can help identify patterns and trends in both the environmental variables and our measurements. Controlled Experiments: In controlled experiments, we intentionally manipulate environmental conditions while keeping other factors constant to observe their direct impact on our measurements. This approach allows us to isolate and quantify the influence of specific environmental factors on our measurements. Machine Learning Techniques: Advanced machine learning algorithms, such as decision trees, random forests, or neural networks, can be trained to predict our measurements based on environmental variables. By analyzing the model's feature importances or coefficients, we can identify which environmental factors are most influential in driving changes in our measurements. Causal Inference Methods: Causal inference techniques aim to establish causal relationships between environmental conditions and our measurements by accounting for potential confounding variables and assessing causality based on observational data. By identifying variations in structural characteristics that differ from typical environmental fluctuations, we can detect structural changes effectively. Stiffness Analysis: With the capability to conduct displacement measurements at any location on the bridge, even in physically hard-to-access areas, we gain a detailed and comprehensive view of the bridge’s structural behavior. This advanced accessibility allows us to collect data in critical and often challenging spots, such as joints, high spans, or internal support sections, where subtle changes in stiffness or displacement may occur but are difficult to monitor through traditional inspections. By capturing this displacement data across all key areas, we can accurately evaluate how the bridge as a whole responds to different loads and identify any localized flexibility or deformation. This data-driven insight enables us to detect early signs of wear or structural change, allowing for proactive maintenance and targeted reinforcements. As a result, we can help ensure that the bridge remains safe, stable, and resilient under a wide range of environmental and operational conditions. Load Analysis: Similarly, we can conduct load analysis across the entire bridge, including locations that are physically hard to access, providing us with valuable insights into how different forces interact with the bridge structure. This enhanced measurement capability allows us to gather data in critical areas, such as support piers, spans, and connections, where varying loads—such as vehicle traffic, wind, and thermal expansion—exert distinct effects. By capturing load data throughout these essential areas, we can accurately assess how forces are distributed across the bridge and pinpoint regions that may experience elevated stress or overloading under certain conditions. This data-driven approach enables us to detect patterns or imbalances in load distribution, which are crucial for understanding the bridge’s overall performance and structural health. Equipped with this information, we can implement timely maintenance, reinforce vulnerable sections, and optimize load management strategies, ultimately ensuring that the bridge remains safe, stable, and resilient under diverse and dynamic operational demands. 8. Airplane Center of gravity The calculation of an airplane's center of gravity (CG) is crucial for several reasons. First, the CG directly affects the aircraft's stability in flight; if it is too far forward or aft, it can lead to poor handling characteristics, making the aircraft difficult to control. A properly balanced aircraft is essential for stable flight and ensures that it responds predictably to control inputs. Additionally, the CG impacts the aircraft’s performance, including takeoff, climb, cruise, and landing, with a well-balanced CG enhancing fuel efficiency, payload capacity, and overall operational efficiency. Safety is another critical factor, as improper CG calculations can lead to dangerous flight conditions such as stalls or excessive pitch, compromising safety during critical phases of flight. Furthermore, aviation regulations require operators to calculate and monitor CG to ensure compliance with safety standards, as failure to adhere to these regulations can result in penalties and increased risk during operations. Finally, the distribution of weight also affects the structural integrity of the aircraft; an imbalanced load can lead to excessive stress on certain components, potentially causing structural failures over time. Overall, accurate calculation of an airplane's CG is essential for ensuring safe and efficient flight operations, maintaining control, optimizing performance, and complying with regulatory standards. The calculation of an airplane's center of gravity (CG) involves determining the weight and distribution of cargo, passengers, fuel, and other onboard factors. While airway bills (AWB) or air consignment notes provide information about the weight and details of the cargo, they are not used directly to calculate the CG. Instead, these documents contribute to weight estimations for the cargo, which are then factored into the overall CG calculation. Relying on estimates, particularly for cargo weight based on documents like the AWB, can lead to errors if the actual weight or distribution differs from what is reported. For more accurate CG calculations, it is ideal to use actual weights obtained from scales rather than estimated weights. Thus, while AWBs play a role, depending solely on them can introduce errors into CG calculations. By using our system, we can measure the weight on each wheel of an airplane as it taxies, allowing us to calculate its center of gravity. This approach has the advantage of not requiring any sensors to be placed on the airplane, providing a direct measurement of its weight and it center of gravity In another embodiment instead of using an airplane bridge we will use the movement of a visual target on the tarmac relative to an inertial frame outside the tarmac to deduce the distribution The distribution of a airplane's weight across each wheel. 9. Weight Distribution in Trains 9.1 Using train bridge As explained before, we can use the motion of a train-bridge to determine the weight and weight distribution across the different wheels of the train cars as they traverse. the bridge. 9.2 Using Deflection of Train Rails or Underlying Structures Subjected to Train Loads as They Pass" Fig.17 illustrates tracking the displacement of a point target on the rail, or or any underlying structure directly subjected to the train load as it passes, in relation to an inertial reference frame as the train cars move, rather than monitoring a bridge, to determine the weight and weight distribution across the different wheels of the train cars as they traverse. 10. Airplane Fuel Gauge and Structural Health Monitoring Fig.18 illustrates measuring the time series displacements of one or several point targets on an airplane wing and on any other compartment that contains fuel reservoirs, that can serve as the basis for monitoring the volume of fuel within them. Their mass changes as fuel is injected into or consumed from these containers. This change in mass alters the structural resonance, which can be deduced by recording the time-series displacement of targets on these structures. In turn, changes in structural resonances alter structural resonance frequencies. By tracking changes in resonance frequencies, we can determine the extent of fuel depletion. As an example, consider that we are measuring the time series displacements of one or several visual targets on an airplane wing in real-time. There are different ways of doing so. One way of doing so consists of having a camera fixed to an airplane body outside the wing to look at the wing. Choosing visual target(s) on the wings and tracking their movement results in time-series displacement for each of them. Such as in Figure 19 is the view captured by the camera used in the live feed deployed in many aircraft (similar field of view could be used for our application) which means the camera location that has already been used for the live feed can be employed for our application. We can conduct this procedure on embodiments beyond the wings, including other parts or compartments of the airplane that contain fuel or fuel reservoirs. As mentioned earlier in contexts like bridge health monitoring, we can integrate environmental variables—such as pressure, altitude, humidity, temperature, and others—into our measurement system to enhance accuracy. This enables us to differentiate between changes caused by environmental factors and those resulting from variations in mass. 10.1 Calculating and monitoring changes in the structural resonance’s frequencies of the wing. One means of doing so is to continuously calculating the power spectrum density of the time-series measurement and thus detecting the resonances frequencies. Variations in resonance frequencies depend on the quantity of fuel consumed. By observing variations in the resonance frequency, we can identify alterations in the structure of the object, and especially its mass. If • M is the mass of the airplane wing • ^^^^M is the changes in its mass, then ΔM = ^^^^.Δ^^^^^^^^• Δ^^^^^^^^is the volume of fuel consumed • ^^^^ is the mass density of the fuel • f is one the structural resonance frequency of the wing • ^^^^f is the changes in resonance frequency then, ^^^^^^^^ = ^^^^.Δ^^^^^^^^^^^^^^^^ ~ ^^^^ ^^^^ This leads to knowing at each moment the volume of fuel consumed and also its consumption profile. Also, by just looking and monitoring the linewidth of resonances in the power spectrum density, we determine the energy dissipation of the wing to the rest of the airplane. Changes in the connection between the body of the airplane with the wing changes the energy dissipation rate of the wing, which changes it structural resonances linewidth. Thus, monitoring, the linewidth of the resonances in the power spectrum density can inform us of any structural malfunctioning between the wind and the body of the airplane 10.2 Method to improve our measurement spatial resolution by one order of magnitude. Use of convolutional neural networks, for example. 11. Applying machine learning algorithms to automate the selection and monitoring of the movement of visual targets on the target structure Leveraging the ability to learn and recognize patterns in visual data using machine learning algorithms such as convolution neural network and track their location form one image frame to the next to deduce. This enables full automation of the system, allowing the machine, once installed, to immediately identify the most suitable visual target within its field of view and begin monitoring its movement automatically. 12. Analysis of mechanical power station / plant, nuclear reactor) A common approach to analyzing the vibration of a mechanical system (such as an engine, vehicle suspension system, or machinery) is to use a spring-mass model.* In mechanical systems like those modeled by the spring-mass approach, a sudden response can often indicate underlying issues with the system's structural management or its dynamic behavior. Figure 20 illustrates our system could be used in real-time by monitoring the time-series displacement of point targets physically in contact with the mechanical system under scrutiny. Sudden changes in phase, frequency, or amplitude could serve as an early warning sign of an issue within the system. Our non-invasive system can be applied to various types of mechanical systems to specifically monitor structures in harsh conditions, including extreme temperatures, high humidity, radiation exposure, confined or inaccessible spaces, or to observe systems that are not suited for direct instrumentation or involve rotating components We can simultaneously conduct real-time spectral and time-series analysis to monitor a range of critical parameters, such as shifts in phase, frequency, resonance, and damping characteristics, as well as intensity variations. This approach also allows us to detect sudden deviations in patterns or unexpected behaviors that differ from previously observed data. By combining these analyses, we gain a deeper insight into both gradual and abrupt changes in system dynamics, enabling rapid identification of anomalies that may indicate potential issues. As an example, there are several approaches to address the issue of monitoring sudden changes in the shape, intensity, frequency, and phase shift of a time series signal. Techniques like the Continuous Wavelet Transform (CWT) are useful for time-frequency analysis, detecting local variations in frequency and shape over time. The Fast Fourier Transform (FFT) and Short-Time Fourier Transform (STFT) help analyze frequency content, identifying shifts in frequency or phase. CUSUM (Cumulative Sum Control Chart) and change-point detection algorithms such as Bayesian Change Point Detection or PELT can detect abrupt shifts in mean, intensity, or other statistical properties. The Hilbert Transform provides instantaneous amplitude and phase information, assisting in phase shift and shape detection. ARIMA models capture dependencies over time, highlighting shifts in signal behavior, while Principal Component Analysis (PCA) helps monitor changes in dominant components. Spectral analysis using Welch’s method tracks changes in frequency distribution, and Dynamic Time Warping (DTW) aligns signals to detect shape or intensity variations. Empirical Mode Decomposition (EMD) decomposes the signal into intrinsic modes to detect shifts in intensity and frequency. Local Outlier Factor (LOF) identifies outliers by analyzing local density, revealing localized anomalies. Finally, Gaussian Process Regression (GPR) models the signal's underlying function to detect deviations from expected patterns. These techniques can be applied individually or in combination to effectively monitor sudden changes in time series data One example where such an idea could be used is in a power plant as illustrated in Figs.21-27: A power plant comprises several key components working together to generate and distribute electricity. It starts with a fuel source—like coal, natural gas, nuclear, or renewables—which powers a boiler or reactor to produce high-pressure steam. This steam drives a turbine, converting thermal energy into mechanical energy, which a generator then transforms into electricity. Afterward, the steam is condensed and cooled in a condenser and cooling system for reuse, enhancing efficiency. Transformers step up the voltage for transmission over power lines, while control systems monitor the entire process to ensure safety and stability. Each component plays a crucial role in the plant’s efficient, reliable operation from energy conversion to electricity delivery. Early detection of a malfunction not only helps prevent the anomaly from quickly spreading to other units, thereby reducing the risk of a larger failure, but also minimizes the need for prolonged shutdowns and costly maintenance, which could affect additional units As an example, let’s consider the interaction between the turbine unit and the generator in a power plant. Changes in the turbine’s rotation relative to its shaft can create significant issues. If this misalignment is not addressed promptly, it can quickly propagate to other components, leading to increased wear, vibrations, and potential system-wide failures. This can extend to the generator, where misalignment may cause damage to bearings, electrical systems, and even lead to a complete shutdown if not detected early. By using our system we can quickly detect such changes, As an example, let's assume we are monitoring visual targets positioned on the exterior of the generator enclosure, with the target points in direct physical contact with the inner aperture of the generator (alternatively, if possible, we could monitor visual targets on the turbine shaft, provided it is not concealed from the outside). The dynamics and vibration of the generator can be modeled as a mass-spring system, where the rotor and stator act as masses, and the springs represent the bearings and supports that resist deformation. The rotation of the turbines around its shaft can then be analyzed as an eccentric force acting on the generator's mass-spring system. This force, due to rotor imbalance or misalignment, creates additional vibrations that can affect the overall stability and performance of the generator. Any change in the turbine’s rotation around its shaft results in a change in the eccentric force within the mass-spring system. This induces changes in the time-series dynamics of the system, which our system can detect. Calculating power density To estimate the power spectral density (PSD) of a signal, we have several methods that vary in complexity, accuracy, and applicability to different types of data. The Fourier Transform is the most common approach, where the PSD is obtained by taking the squared magnitude of the Fourier coefficients. However, for signals that are short or noisy, we can use Welch’s Method, which splits the signal into overlapping segments, computes the Fourier transform on each segment, and averages the results. This smooths out noise and is particularly helpful for improving PSD estimates in noisy data. Alternatively, the Autocorrelation Method, based on the Wiener-Khinchin theorem, computes the autocorrelation function and then takes its Fourier transform to obtain the PSD. This method is effective for stationary signals by focusing on the correlation structure instead of the direct signal data. The Periodogram is another direct method where the PSD is estimated by squaring the magnitude of the Fourier transform; though straightforward, it is often noisy without additional averaging. For higher-resolution spectral estimates, Filter Bank Methods pass the signal through a set of bandpass filters that isolate various frequency components, with wavelet transforms providing multiresolution analysis, especially for non-stationary signals. Parametric Methods, such as Autoregressive (AR) and Moving Average (MA) models, assume the signal can be represented by a statistical model. The PSD is then derived from the model parameters, allowing for smooth spectral estimates even in noisy or short signals. Wavelet Transform-Based Methods analyze both time and frequency simultaneously, capturing spectral information for non-stationary signals by computing energy at various scales, useful in applications where signal frequency components vary over time. Capon’s Method, or minimum variance distortionless response (MVDR), is a high-resolution adaptive method that sharpens spectral peaks, commonly used in radar and sonar. Finally, the Burg Method, a type of AR model, estimates PSD by minimizing forward and backward prediction errors, achieving high spectral resolution ideal for resolving closely spaced spectral lines. Each of these methods offers unique strengths, making them suitable for different data types and application requirements. Experimental Results and Implementations. Figure 28 illustrates an example system 2800 for monitoring a structure or device under test, comprising an electrooptic device including a camera 2802 for capturing images of the visual target on the bridge from which time series displacement of the target can be determined. The system further comprises a computer 2804 for receiving video footage of the traffic (from traffic camera 2806) on the structure and determining the time series displacement of the target from the images of the visual target captured by the camera. The system can be either portable or fixed and is very easy to deploy in just a few minutes. It is highly portable and can be discreetly deployed. Once calibrated for a specific structure—taking into account factors such as the location and position of the cameras relative to the structure, among others—it can reuse the same calibration settings from previous deployments. Figs.33-39 illustrate measurements of the time series displacement of the target on a civil structures obtained from the camera set ups in Figs.29-31. Figure 40 illustrates measured out of plane displacement from a camera of Fig, 19 observing visual targets on the wing of Figure 18. Figure 41 shows the power spectrum of the displacement in Figure 40. Hardware environment FIG.42 is an exemplary hardware and software environment 4200 (referred to as a computer-implemented system and / or computer-implemented method) used to implement one or more embodiments of the invention by processing data from sensors (e.g. acoustic or camera) of targets on the structure under test and / or traffic camera 4228. The hardware and software environment includes a computer 4202 and may include peripherals. Computer 4202 may be a user / client computer, server computer, or may be a database computer. The computer 4202 comprises a hardware processor 4204A and / or a special purpose hardware processor 4204B (hereinafter alternatively collectively referred to as processor 4204) and a memory 4206, such as random access memory (RAM). The computer 4202 may be coupled to, and / or integrated with, other devices, including input / output (I / O) devices such as a keyboard 4214, a cursor control device 4216 (e.g., a mouse, a pointing device, pen and tablet, touch screen, multi-touch device, etc.) and a printer. In one or more embodiments, computer 4202 may be coupled to, or may comprise, a portable or media viewing / listening device 4232 (e.g., an MP3 player, IPOD, NOOK, portable digital video player, cellular device, personal digital assistant, etc.). In yet another embodiment, the computer 4202 may comprise a multi-touch device, mobile phone, gaming system, internet enabled television, television set top box, or other internet enabled device executing on various platforms and operating systems. In one embodiment, the computer 4202 operates by the hardware processor 4204A performing instructions defined by the computer program 4210 (e.g., a structure under test monitoring application) under control of an operating system 4208. The computer program 4210 and / or the operating system 4208 may be stored in the memory 4206 and may interface with the user and / or other devices to accept input and commands and, based on such input and commands and the instructions defined by the computer program 4210 and operating system 4208, to provide output and results. Output / results may be presented on the display 4222 or provided to another device for presentation or further processing or action. In one embodiment, the display 4222 comprises a liquid crystal display (LCD) having a plurality of separately addressable liquid crystals. Alternatively, the display 4222 may comprise a light emitting diode (LED) display having clusters of red, green and blue diodes driven together to form full-color pixels. Each liquid crystal or pixel of the display 4222 changes to an opaque or translucent state to form a part of the image on the display in response to the data or information generated by the processor 4204 from the application of the instructions of the computer program 4210 and / or operating system 4208 to the input and commands. The image may be provided through a graphical user interface (GUI) module 4218. Although the GUI module 4218 is depicted as a separate module, the instructions performing the GUI functions can be resident or distributed in the operating system 4208, the computer program 4210, or implemented with special purpose memory and processors. In one or more embodiments, the display 4222 is integrated with / into the computer 4202 and comprises a multi-touch device having a touch sensing surface (e.g., track pod, touch screen, smartwatch, smartglasses, smartphones, laptop or non- laptop personal mobile computing devices) with the ability to recognize the presence of two or more points of contact with the surface. Examples of multi-touch devices include mobile devices (e.g., IPHONE, ANDROID devices, WINDOWS phones, GOOGLE PIXEL devices, NEXUS S, etc.), tablet computers (e.g., IPAD, HP TOUCHPAD, SURFACE Devices, etc.), portable / handheld game / music / video player / console devices (e.g., IPOD TOUCH, MP3 players, NINTENDO SWITCH, PLAYSTATION PORTABLE, etc.), touch tables, and walls (e.g., where an image is projected through acrylic and / or glass, and the image is then backlit with LEDs. Some or all of the operations performed by the computer 4202 according to the computer program 4210 instructions may be implemented in a special purpose processor 4204B. In this embodiment, some or all of the computer program 4210 instructions may be implemented via firmware instructions stored in a read only memory (ROM), a programmable read only memory (PROM) or flash memory within the special purpose processor 4204B or in memory 4206. The special purpose processor 4204B may also be hardwired through circuit design to perform some or all of the operations to implement the present invention. Further, the special purpose processor 4204B may be a hybrid processor, which includes dedicated circuitry for performing a subset of functions, and other circuits for performing more general functions such as responding to computer program 4210 instructions. In one embodiment, the special purpose processor 4204B is an application specific integrated circuit (ASIC), field programmable gate array, graphics processing unit (GPU), or multi core processor for parallel processing, or processor configured for machine learning, artificial intelligence, or neural networks. The computer 4202 may also implement a compiler 4212 that allows an application or computer program 4210 written in a programming language such as C, C++, Assembly, SQL, PYTHON, PROLOG, MATLAB, RUBY, RAILS, HASKELL, or other language to be translated into processor 4204 readable code. Alternatively, the compiler 4212 may be an interpreter that executes instructions / source code directly, translates source code into an intermediate representation that is executed, or that executes stored precompiled code. Such source code may be written in a variety of programming languages such as JAVA, JAVASCRIPT, PERL, BASIC, etc. After completion, the application or computer program 4210 accesses and manipulates data accepted from I / O devices and stored in the memory 4206 of the computer 4202 using the relationships and logic that were generated using the compiler 4212. The computer 4202 also optionally comprises an external communication device such as a modem, satellite link, Ethernet card, or other device for accepting input from, and providing output to, other computers 4202. In one embodiment, instructions implementing the operating system 4208, the computer program 4210, and the compiler 4212 are tangibly embodied in a non- transitory computer-readable medium, e.g., data storage device 4220, which could include one or more fixed or removable data storage devices, such as a zip drive, floppy disc drive 4224, hard drive, CD-ROM drive, tape drive, etc. Further, the operating system 4208 and the computer program 4210 are comprised of computer program 4210 instructions which, when accessed, read and executed by the computer 4202, cause the computer 4202 to perform the steps necessary to implement and / or use the present invention or to load the program of instructions into a memory 4206, thus creating a special purpose data structure causing the computer 4202 to operate as a specially programmed computer executing the method steps described herein. Computer program 4210 and / or operating instructions may also be tangibly embodied in memory 4206 and / or data communications devices 4230, thereby making a computer program product or article of manufacture according to the invention. As such, the terms “article of manufacture,” “program storage device,” and “computer program product,” as used herein, are intended to encompass a computer program accessible from any computer readable device or media. Of course, those skilled in the art will recognize that any combination of the above components, or any number of different components, peripherals, and other devices, may be used with the computer 4202. FIG.43 schematically illustrates a typical distributed / cloud-based computer system 4300 using a network 4304 to connect client computers 4302 to server computers 4306. A typical combination of resources may include a network 4304 comprising the Internet, LANs (local area networks), WANs (wide area networks), SNA (systems network architecture) networks, or the like, clients 4302 that are personal computers or workstations (as set forth in FIG.42), and servers 4306 that are personal computers, workstations, minicomputers, or mainframes (as set forth in FIG. 42). However, it may be noted that different networks such as a cellular network (e.g., GSM [global system for mobile communications] or otherwise), a satellite based network, or any other type of network may be used to connect clients 4302 and servers 4306 in accordance with embodiments of the invention. A network 4304 such as the Internet connects clients 4302 to server computers 4306. Network 4304 may utilize ethernet, coaxial cable, wireless communications, radio frequency (RF), etc. to connect and provide the communication between clients 4302 and servers 4306. Further, in a cloud-based computing system, resources (e.g., storage, processors, applications, memory, infrastructure, etc.) in clients 4302 and server computers 4306 may be shared by clients 4302, server computers 4306, and users across one or more networks. Resources may be shared by multiple users and can be dynamically reallocated per demand. In this regard, cloud computing may be referred to as a model for enabling access to a shared pool of configurable computing resources. Clients 4302 may execute a client application or web browser and communicate with server computers 4306 executing web servers 4310. Such a web browser is typically a program such as MICROSOFT INTERNET EXPLORER / EDGE, MOZILLA FIREFOX, OPERA, APPLE SAFARI, GOOGLE CHROME, etc. Further, the software executing on clients 4302 may be downloaded from server computer 4306 to client computers 4302 and installed as a plug-in or ACTIVEX control of a web browser. Accordingly, clients 4302 may utilize ACTIVEX components / component object model (COM) or distributed COM (DCOM) components to provide a user interface on a display of client 4302. The web server 4310 is typically a program such as MICROSOFT’S INTERNET INFORMATION SERVER. Web server 4310 may host an Active Server Page (ASP) or Internet Server Application Programming Interface (ISAPI) application 4312, which may be executing scripts. The scripts invoke objects that execute business logic (referred to as business objects). The business objects then manipulate data in database 4316 through a database management system (DBMS) 4314. Alternatively, database 4316 may be part of, or connected directly to, client 4302 instead of communicating / obtaining the information from database 4316 across network 4304. When a developer encapsulates the business functionality into objects, the system may be referred to as a component object model (COM) system. Accordingly, the scripts executing on web server 4310 (and / or application 4312) invoke COM objects that implement the business logic. Further, server 4306 may utilize MICROSOFT’S TRANSACTION SERVER (MTS) to access required data stored in database 4316 via an interface such as ADO (Active Data Objects), OLE DB (Object Linking and Embedding DataBase), or ODBC (Open DataBase Connectivity). Generally, these components 4300-4316 all comprise logic and / or data that is embodied in / or retrievable from device, medium, signal, or carrier, e.g., a data storage device, a data communications device, a remote computer or device coupled to the computer via a network or via another data communications device, etc. Moreover, this logic and / or data, when read, executed, and / or interpreted, results in the steps necessary to implement and / or use the present invention being performed. Although the terms “user computer”, “client computer”, and / or “server computer” are referred to herein, it is understood that such computers 4302 and 4306 may be interchangeable and may further include thin client devices with limited or full processing capabilities, portable devices such as cell phones, notebook computers, pocket computers, multi-touch devices, and / or any other devices with suitable processing, communication, and input / output capability. Of course, those skilled in the art will recognize that any combination of the above components, or any number of different components, peripherals, and other devices, may be used with computers 4302 and 4306. Embodiments of the invention are implemented as a software / monitoring application on a client 4302 or server computer 4306. Further, as described above, the client 4302 or server computer 4306 may comprise a thin client device or a portable device that has a multi-touch-based display. References The following references are incorporated by reference herein. [1] US Patent Publication No.20190293518 entitled “New autonomous electro-optical system to monitor in real-time the full spatial motion (rotation and displacement) of civil structures,” patent applcation serial no. 16 / 359,754, by Shervin Taghavi, providing further information on an electro-optic device for measuring displacement of visual targets on a structure as described herein. Process Steps Fig.44 illustrates a method of making a system. Block 4400 represent providing or programming a computer implemented system 4200 comprising: (a) a computer 4202 having one or more memories; (b) one or more processors 4204 executing on the computer; (c) the one or more memories storing a set of instructions, wherein the set of instructions, when executed by the one or more processors cause the one or more processors to perform operations comprising: receiving or obtaining sensor data comprising one or more displacements as a function of time 3400, 4000of one or more targets 1700, 500, 1-4 (in Figure 18), 2600, 2602 attached to a structure 502, 106, 2604, 2606 in response to point loads Wid applied to the structure; optionally receiving image data representing images 1400 of the vehicles 1402 comprising the point loads traversing the structure; determining, from the displacements, at least one of: a health status of the structure, or forces F or intensities of forces F applied by one or more of the point loads by: obtaining a model for the displacements as a function of a forces applied by the point loads, wherein the model models the displacements as a superposition of responses of the structure to the one or more point loads at each of one or more coordinate locations 902 in a virtual coordinate grid 900 superimposed / associated with / connected on an image of structure; and solving or deducing the model for the forces as an inverse problem using the coordinate locations of the point loads and the displacements obtained from the image data and the sensor data respectively. Block 4402 represents optionally coupling a sensor for capturing the sensor data and a camera for capturing the image data to the computer. Block 4406 represents the end result. The system can be embodied in many ways including, but not limited to, the following. 1. A computer implemented system comprising: (a) a computer having one or more memories; (b) one or more processors executing on the computer; (c) the one or more memories storing a set of instructions, wherein the set of instructions, when executed by the one or more processors cause the one or more processors to perform operations comprising: receiving obtaining sensor data comprising one or more displacements as a function of time of one or more targets attached to a structure in response to point loads applied to the structure; optionally receiving image data representing images of the vehicles comprising the point loads traversing the structure; determining, from the displacements, at least one of: a health status of the structure, or forces applied by one or more of the point loads by: obtaining a model for the displacements as a function of a forces applied by the point loads, wherein the model models the displacements as a superposition of responses of the structure to the one or more point loads at each of one or more coordinate locations in a virtual coordinate grid superimposed on the structure; and solving or deducing the model for the forces as an inverse problem using the coordinate locations of the point loads and the displacements obtained from the image data and the sensor data respectively. 2. The system of clause 1, wherein each of a plurality of individual cell in the grid are small enough to distinguish between the point loads comprising wheels of the vehicle. 3. The system of clause 1 or 2, wherein the operations comprise: determining the displacements as a function of time from the sensor data comprising images of the target comprising a visual target; obtaining an impulse response h(t) comprising components or coefficients at each coordinate location that are time dependent due to motion of the point loads and determining from the image data matched to the coordinate grid which coefficients or components are activated by application of the point load; and deducing or determining the forces or intensities of the point loads from the model relating the known displacements as a function of time to the intensities the known impulse response h(t) 4. The system of any of the clauses 1-3, wherein the model comprises a calibrated impulse response function of the structure comprising calibrated impulse response coefficients hxyat each of the coordinate locations x,y, the hxycoefficient relating a contribution to the displacements of one or more targets to the one or more point loads as they traverse the location x,y. 5. The system of any of the clauses 1-4, wherein the computer: receives the displacements comprising a time series of displacements over a measurement window or time segment, each of the displacements associated with a different time stamp; receives the image data representing a time series of images of the vehicles traversing the bridge; identifies the coordinate locations of the point loads of the vehicles at each of the time stamps; and determines the one or more forces at one or more of the coordinate locations using the calibrated response function. 6. The system of any of the clauses 1-5, wherein the solving comprises solving the model comprising a system of simultaneous linear equations in a matrix equation: D = A multiplied by W where matrix D contains the measurements of the displacement of the targets on the structure at each time instant in a measurement window or time segment as obtained from the sensor data; matrix W comprises a vector matrix ^^^^2,.., ^^^^^^^^,.., ^^^^^^^^represent thedistinguishable point loads applied at the coordinate , ^^^^^^^^(^^^^))over thetime segment; and matrix A comprises the spatial-temporal values associated with each of the point loads applied during this time segment; wherein:^^^^^^^^^^^^^^^^^^^^ ℎ(^^^^^^^^(^^^^), ^^^^^^^^(^^^^)) the impulse response coefficient associated with thecoordinate location (^^^^^^^^(^^^^), ^^^^^^^^(^^^^))then, the matrix A can be defined as: )so that ^^^^^^^^,^^^^represents the value in row t (time step) and column s (point load) in matrix A. and matrix A provides a temporal snapshot of each of the point loads ^^^^^^^^applied at a coordinate location over time as obtained from the image data; and the equation is solved to calculate the unknown forces comprising Wn given knowledge of A and D from the image data and sensor data respectively. 7. Figs.10-14a illustrate an example of the system of any of the clauses 1-6, wherein the operations further include an object tracking algorithm that identifies a number and positioning of the point loads on each of the vehicles and tracks each of the point loads as the vehicles move across the structure during a measurement window 3300 with a unique identifier tag (179, 182 in Fig.14a). 8. Fig.10-14a illustrate an example of the system of any of the clauses 1- 7, comprising the operations identifying the point loads comprising wheels 1000 associated with each of the vehicles that have entered a pre-selected region of interest ROI in a field of view of a single camera observing the structure, by comparing spacings between the wheels to known spatial relationships in the image data, assuming the wheels on a common axle are perpendicular to the direction of travel of the vehicle, and wheels on one side of the vehicle are colinear with a direction of travel of the vehicle. 9. The computer system of clause 8, wherein the computer uses machine learning to identify the wheels. 10. The computer system of any of the clauses 1-5 or 7-9, wherein the model comprises curve fitting and the forces are fitting parameters to the curves used to fit the time series of the displacements. 11. Fig.46 and 47 illustrates an example of the system of any of the clauses 1-5 or 7-10, further comprising: receiving the displacements comprising a time series of displacements over a measurement window or time segment, each of the displacements associated with a different time stamp; and the model comprising a neural network 602 comprising: a plurality of inputs (pixel 1… Pixel N), each of the inputs for receiving an intensity of one of the forces applied by point loads at a different one of each of the coordinate locations 702 of the point loads in coordinate grid 700, a plurality of outputs (point target 1 deflection), each of the outputs for outputting displacement of the targets measured at a given one of the time stamps in the measurement window, and one or more layers 604 of interconnected nodes 606 connecting the inputs to the outputs, wherein weighted connections between the nodes and activation functions at the nodes are determined through training with training data so that the layers accurately associate known ones of the intensities of the forces inputted at the inputs, through the weighted connections and the activation functions, to measured displacements at the outputs; and the computer operating the trained neural network in reverse working backward from the time series of displacements at the outputs to determine, as an inverse problem, the appropriate intensities at the inputs that are associated with the displacements. 12. Fig.14 illustrates an example the system 1410 of any of the clauses 1- 11, further comprising monitoring changes in the displacements over time and associating abnormal changes in the displacements with a change in health status of the structure. 13. Fig.16 illustrates an example of the system of clause 12, wherein the operations include performing analysis of the time series of displacement in frequency domain and time domain (dynamic and transient response) (e.g., determines a power spectrum of the time series of the displacements) to determine at least one of resonance modes 1600 of the structure, a stiffness of the structure, linewidth of the resonance modes, or a phase shift of the time series of displacements. 14. The system of clause 12 or 13, wherein the operations: associate changes in the resonance modes or stiffness of the structure with structural changes in the structure and compares the changes with a model to determine if the changes correlate with those expected for environmental ambient changes, such as weather, or those expected for changes in a health status of the structure; and / or determines a linewidth of one or more peaks of the resonant modes and associates changes in the linewidth with changes in energy dissipation to an environment of the structure or structural damping changes. 15. The system of any of the clauses 1-14, wherein the structure comprises a bridge, a road, or a component of a power plant. 16. The computer system of any of the clauses 1-15, wherein the calibrated impulse response function coefficients are those that relate the time series of the displacements with known intensities of point loads at each of the coordinate locations. 17. The computer system of any of the clauses 1-16, wherein the calibrated response functions are updated to account for effects of weather (e.g., obtained using meteorological information, and comparing obtained properties as a function of weather (e.g., temperature) or other environmental impacts on structural changes (mass, stiffness, resonance characteristics, damping) of the structure. 18. Figs.1-3, 8a and 10-14a illustrate examples of the computer system of any of the clauses 1-17, wherein the vehicle comprises at least one of a car, a truck, a train, an airplane, or one or more pedestrians and the structure comprises a bridge or a road. 19. Figs.4-7 illustrate examples of the computer system of any of the clauses 1-18, wherein the target comprises a stain, catseye, roadmarker 502, a specialized layer of pavement applied to the road surface having a stiffness that enhances the displacement in response to passage of the point loads. 20. The computer system of any of the clauses 1-19, wherein the computing system learns to identify the targets comprising visual targets and deduce the time series displacement of the visual targets by tracking their location on each image frame of the images using machine learning. 21. The system of clause 20, wherein different types of object detection methods are utilized to determine the location of the same visual target , thereby assessing the error associated with the algorithm. 22. The system of clause 20 or 21 wherein the system automatically selects the target by utilizing pre-trained images of the target comprising typical visual features, such as stains, marks, and other characteristics commonly found on the structure. 23. The computing system of any of the clauses 1-22 using Super- Resolution Convolutional Neural Networks (SRCNNs) to improve the spatial resolution of the image data through advanced algorithmic super-resolution techniques to increase the spatial resolution of the measurement of the displacements. 24. A system for monitoring the structure of any of the clauses 1-23, further comprising at least of a sensor coupled to the structure for measuring the displacements or a camera coupled to the structure for capturing the images comprising the image data; and the computer system coupled to at least one of the sensor or the camera. 25. The system of any of the clauses 1-24, wherein the operations further comprise outputting an aggregation of the forces applied by the point loads, traffic information comprising a number of the vehicles, weather at the structure, health status of the structure, and lifetime of the structure. 26. A monitoring system 4500 , comprising: one or more sensors positioned for capturing electromagnetic signals or acoustic signals transmitted from a structure of a structure under test; and a computer system configured for: determining, from the signals, the displacement of one or more targets on the structure as a function of time; obtaining a model for the displacement as a function of load distribution on the structure, and solving the model for the load distribution as an inverse problem using the displacement as a known data. 27. `The system 2000 of clause 26, wherein the structure is a component of a power plant 2100. 28. The system of any of the clauses 15 or 26-27, wherein power plant comprises a turbine 2200 comprising a turbine shaft 2204 coupled to generator 2202, and the signals are transmitted from a target 2602, 2600 located on the generator, the turbine; a case of the generator which is physically attached to the generator or the target at an interface between the turbine shaft and an entrance of the generator. 29. The system of any of the clauses 26-28 comprising a fuel gauge, wherein the structure is a wing 1800 or fuselage on an aircraft or airplane 300 and the computer determines, from the load distribution, a fuel level in a tank stored in the wing or fuselage. 30. The system of any of the clauses 26-29, further comprising obtaining a power spectrum 4100 of the displacements 4000 wherein the model for the displacement comprises relating the power spectrum, comprising resonance modes of the wing, to the fuel level. 31. The system of clause 26 monitoring the structure comprising a wing / fuselage connection of an airplane. 32. The system of any of the clauses 1-31, further comprising the operations comprising: calculating dynamic and steady state components of the forces as the point loads comprising wheels traverse the structure; using the dynamic and steady state components to analyze behavior of the vehicle’s suspension system comprising individual wheel suspension systems 1420; and deductively deriving a suspension characteristics of the vehicle by evaluating the responses of the individual wheel suspension system to the point loads. In one embodiment, using the average to obtain the static force, and analyzing the oscillations to characterize the suspension- i.e., damped oscillations give a damping constant. In one embodiment, performing a frequency analysis of (e.g., observing oscillations in) the forces; e.g., steady state (static weight at rest) is obtained using a low pass filter, a bandpass filter for dynamic response (suspension at speed), or take power spectrum density, to obtain characteristic information on the vehicle or working operation of the suspension and damping. 33. A computer implemented method for determines the input loads applied to a structure comprising: analyzing, in the computer; displacement of target(s) on the structure, utilizing the structure’s impulse response, along with known trajectory of each of the input load, speed and acceleration of each of the loads along the trajectory, to obtain the input loads, where the displacement is a function of input location of each of the loads and is influenced by at least one of the point load’s speed or acceleration, or a combination of both. 34. The method of clause 33, wherein the impulse response is associated with a coordinate grid and the input loads are determined by reversing propagation through a neural network whose inputs comprise a vector that comprises multiple variables, including intensity of the load, speed of the load, acceleration of the load, and at least one of another characteristic of the load, or dynamic behavior of the bridge 35. The method of clause 33 or 34, where the system’s impulse response ateach grid location i,j is time dependent and comprises ℎ^^^^,^^^^ (^^^^)36. A computing system for determining time series displacement of visual target on the target structure by leveraging the ability to learn and recognize patterns in visual data using machine learning algorithms and deduce the time series displacement of the visual target by tracking their location on each image frame. 37. The system of clause 36, wherein different types of object detection methods are utilized to determine the location of the same object, thereby assessing the error associated with the algorithm. 38. The system of clause 36 wherein the system automatically selects a visual target by utilizing pre-trained images of typical visual features, such as stains, marks, and other characteristics commonly found on the structure of interest. 39. A computing system calculating time series displacement of visual target(s) that employs Super-Resolution Convolutional Neural Networks (SRCNNs) to improve the spatial resolution of images through advanced algorithmic super- resolution techniques to increase the spatial resolution of the measurement. ─This approach contrasts with conventional digital zooming methods that use linear interpolation. Linear interpolation estimates new pixel values by averaging neighboring pixels, which can degrade image quality. This degradation happens because pixels are digitally enlarged to fill gaps, rather than optically adjusting the lens, which maintains better image fidelity.─ 41. A monitoring system for determining one or more identifying health status and / or vehicle information for traffic traversing a bridge, comprising: a plurality of sensor devices positioned for capturing electromagnetic signals or acoustic signals transmitted from a bridge; and a computer system configured for: receiving meteorological data of weather from one or more meteorological stations at or near the bridge; determining, from the signals, a displacement of the bridge as a function of time; and correlating or finding a relationship between the displacement and the meteorological data; and determining whether changes in the displacement are due to changes in the weather or those caused by structural alterations of the bridge related to health of the bridge or vehicles traversing the bridge. 42. The system of clause 41, wherein the computer system determines displacements in the bridge due to traffic traveling on the bridge (Traffic displacements) and calibrates the displacements used to measure a health status of the bridge using the traffic displacements. 43. The system of clause 41 or 42, wherein the computer system determines point loads traveling on the bridge from the displacements while taking account (e.g., subtracting) those displacements caused by the weather or structural alterations of the bridge. 44. A vehicle monitoring system for determining center of gravity of one or more vehicles traversing a bridge, comprising: a plurality of sensor devices positioned for capturing electromagnetic signals or acoustic signals transmitted from a bridge and / or one or more vehicles comprising point loads traversing the bridge; and a computer system configured for: determining, from the signals: a displacement of the bridge in response to one or more of the point loads traversing the bridge as a function of time; and one or more locations of the one or more point loads traversing the bridge as a function of time; obtaining a model for the displacement as a function of a weight distribution of the point loads, wherein the model models the displacement as a superposition of responses caused by each of the one or more point loads at the locations; and solving the model for the weight distribution as an inverse problem using the displacement and the locations obtained from the signals; and calculating the center of gravity of the vehicles from the weight distribution. 45. The system of clause 44, wherein the vehicle comprises an aircraft or airplane taxiing on the bridge. 46. A vehicle monitoring system for determining center of gravity of one or more vehicles traversing a bridge, comprising: a plurality of sensor devices positioned for capturing electromagnetic signals or acoustic signals transmitted from a bridge and / or one or more vehicles comprising point loads traversing the bridge; and a computer system configured for: determining, from the signals: a displacement of the bridge in response to one or more of the point loads traversing the bridge as a function of time; and one or more locations of the one or more point loads traversing the bridge as a function of time; obtaining a model for the displacement as a function of a weight distribution of the point loads, wherein the model models the displacement as a superposition of responses caused by each of the one or more point loads at the locations; and solving the model for the weight distribution as an inverse problem using the displacement and the locations obtained from the signals; and calculating the center of gravity of the vehicles from the weight distribution. 47. The system of clause 46, wherein the vehicle comprises an aircraft or airplane taxiing on the bridge. 48. A vehicle monitoring system for determining center of gravity of one or more vehicles traversing a bridge, comprising: a plurality of sensor devices positioned for capturing electromagnetic signals or acoustic signals transmitted from a bridge and / or one or more vehicles comprising point loads traversing the bridge; and a computer system configured for: determining, from the signals: a displacement of the bridge in response to one or more of the point loads traversing the bridge as a function of time; and one or more locations of the one or more point loads traversing the bridge as a function of time; obtaining a model for the displacement as a function of a weight distribution of the point loads, wherein the model models the displacement as a combination of responses caused by each of the one or more point loads at the locations; and solving the model for the weight distribution as an inverse problem using the displacement and the locations obtained from the signals; and calculating the center of gravity of the vehicles from the weight distribution. 49. The system of clause 48, wherein the vehicle comprises an aircraft or airplane taxiing on the bridge. 50. A vehicle monitoring system for determining one or more identifying characteristics of one or more vehicles traversing a pavement (road), comprising: a plurality of sensor devices positioned for capturing electromagnetic signals or acoustic signals transmitted from a target or marker on the pavement; and a computer system configured for: determining, from the signals: a displacement of the road in response to one or more of the point loads traversing the road as a function of time; and one or more locations of the one or more point loads traversing the road as a function of time; obtaining a model for the displacement as a function of a weight distribution of the point loads, wherein the model models the displacement as a combination of responses caused by each of the one or more point loads at the locations; and solving the model for the weight distribution as an inverse problem using the displacement and the locations obtained from the signals. 51. The system of clause 50, wherein the vehicle comprises a car, truck, or airplane, train etc.. any type of load 52. A vehicle monitoring system for determining one or more identifying characteristics of one or more vehicles traversing a bridge, comprising: a plurality of sensor devices positioned for capturing electromagnetic signals or acoustic signals transmitted from a roadway or pavement and / or one or more vehicles comprising point loads traversing the roadway or pavement; and a computer system configured for: determining, from the signals: a displacement of the bridge in response to one or more of the point loads traversing the bridge as a function of time; and one or more locations of the one or more point loads traversing the bridge as a function of time; obtaining a model for the displacement as a function of a magnitude of each of the point loads, wherein the model models the displacement as a sum of impulse function responses of the bridge (Green’s functions) caused by each of the one or more point loads applied at the locations; and solving the model for the magnitudes as an inverse problem using the displacement and the locations obtained from the signals. 53. The system of any of the clauses wherein the model is a mathematical relationship: where d is the displacement as a function of time, Wjis the magnitude of the force applied by the jth one of the point load and h is the impulse function at each of the locations of the point loads. 54. The system of clause 53, wherein the relationship is expressed as a matrix equation and the solving comprises solving the matrix equation �^^^^ = (^^^^^^^^^^^^)−^^^^^^^^^^^^^^^^ where W is the matrix containing the magnitude of each of the point loads, D is the matrix containing the measured time series of displacements, and A is a matrix derived from the impulse responses corresponding to an identifiable point load at a location at time ^^^^^^^^obtained form measurements (e.g., video images of the traffic) traversing the bridge. 55. The system of clause 54 or 53, wherein the relationship is expressed as a matrix equation and the solving comprises solving the matrix equation ^^^^ = (^^^^^^^^^^^^)−^^^^^^^^^^^^^^^^where W is the matrix containing the magnitude of each of the point loads, D is the matrix containing the measured time series of displacements, and A is a matrix derived from the impulse responses corresponding to an identifiable point load at a location at time ^^^^^^^^obtained form measurements (e.g., video images of the traffic) traversing the bridge. 56. The system of any of the clauses wherein the system's impulse response is calculated using sparse inputs but without knowing their exact intensities using: • Blind system identification involves identifying system properties without precise knowledge of the input signals. • Sparse excitation refers to the input being sparse or limited in some manner, but its exact magnitude is not known. 57. A vehicle monitoring system for determining center of gravity of one or more vehicles traversing a bridge, comprising: a plurality of sensor devices positioned for capturing electromagnetic signals or acoustic signals transmitted from a roadway and / or one or more vehicles comprising point loads traversing the roadway; and a computer system configured for: determining, from the signals: a displacement of the bridge in response to one or more of the point loads traversing the roadway as a function of time; and one or more locations of the one or more point loads traversing the roadway as a function of time; obtaining a model for the displacement as a function of a weight distribution of the point loads, wherein the model models the displacement as a combination of responses caused by each of the one or more point loads at the locations; and solving the model for the weight distribution as an inverse problem using the displacement and the locations obtained from the signals; and calculating the center of gravity of the vehicles from the weight distribution. The system of clause 58, wherein the vehicle comprises an aircraft or airplane taxiing 58. A fuel gauge system, comprising: a plurality of sensor devices positioned (e.g., on the vehicle or remote from the vehicle) for capturing electromagnetic signals or acoustic signals transmitted one or more structures (e.g., wing, fuselage) of a vehicle containing a fuel tank; and a computer system configured for: determining, from the signals: the displacement of the structures as a function of time; and obtaining a model (e.g., for resonance frequency, damping) for the displacement as a function of a fuel content in the tank, and solving the model for the fuel content as an inverse problem using the displacement as a known data. 59. The fuel gauge of clause 58, wherein the vehicle comprises an airplane or aircraft. 60. The system of clause 58 to monitor wing / fuselage connection of an airplane 61. The method of any of the clauses 33-35, further comprising estimating the speed and acceleration from a traffic feed obtained using a camera and using the estimate as a baseline for further refinement of the speed and acceleration. 62. The method of any of the clauses 33-35 or 36 implemented using the system of any of the clauses 1-32. 63. The method or computer system of any of the clauses wherein the computer system comprises (a) a computer having one or more memories; (b) one or more processors executing on the computer; (c) the one or more memories storing a set of instructions, wherein the set of instructions, when executed by the one or more processors cause the one or more processors to perform the operations described in the clause. 64. The system or computer system of any of the clauses, wherein the computer comprise a non-transitory computer readable medium storing a plurality of instructions, the plurality of instructions described in the clauses. Fig.45 and 46 illustrates example systems 100 comprising sensors 102 and computer system 104. In one or more embodiments, the system does all outputting vehicle weight, traffic (number of cars) , health status structure, and weather, lifetime of structure, The information may be useful for pavement analysis- want to know amount of load, on pavement, when and where load is applied using pavement analysis aggregating information in one system. In various embodiments, the system(s) can be either portable (deployable and removable) or fixed / permanent and is very easy to deploy in just a few minutes. It is highly portable and can be discreetly deployed. Once calibrated for a specific structure—taking into account factors such as the location and position of the cameras relative to the structure, among others—it can reuse the same calibration settings from previous deployments. Data can be outputted from the systems to web applications or inputted to the system from web applications. Method Fig.48 is a flowchart illustrating a method of monitoring and collecting data about a structure, comprising the following steps. Block 4800 represents capturing sensor data from a structure using o ne or more sensors. Block 4802 represents receiving or obtaining the sensor data comprising one or more displacements as a function of time of one or more targets attached to a structure in response to point loads applied to the structure;optionally receiving image data representing images of the vehicles comprising the point loads traversing the structure. Block 4804 represents determining (e.g., calculating, deducing), from the displacements, at least one of: a health status of the structure, or forces applied by one or more of the point loads by: obtaining a model for the displacements as a function of a forces applied by the point loads, wherein the model models the displacements as a superposition of responses of the structure to the one or more point loads at each of one or more coordinate locations in a virtual coordinate grid superimposed on the structure; and solving or deducing the model for the forces as an inverse problem using the coordinate locations of the point loads and the displacements obtained from the image data and the sensor data respectively. The method of Fig.48 implemented using the system of any of the clauses 1- 32. In one or more examples we can determine Impulse Response Without Known Inputs. For example, We can identify a system's impulse response using sparse inputs but without knowing their exact intensities using: (1) Blind system identification: involves identifying system properties without precise knowledge of the input signals. (2) Sparse excitation: refers to the input being sparse or limited in some manner, but its exact magnitude is not known. Example Advantages and Improvements We have demonstrated a non-invasive method that enables the collection of extensive, comprehensive data on various types of vehicles—such as airplanes, cars, trucks, trains, and others—as well as pedestrians, which was previously unavailable. Our system is stealthy, quick to deploy, and lightweight, allowing easy transport. It is designed to operate reliably in real-world environmental conditions. All the data collected can be processed and displayed in real time on a web application, accessible to anyone with the appropriate permissions, anywhere. It relies on measuring the time-series dynamics and transients of point targets on the road or supporting structures, such as bridges, rails (or their underlying supporting structures), airplane tarmacs, airplane bridges, and others, where the displacement of the supporting structure, pavement and etc. is directly affected by the passage of vehicles or external point loads traversing the road or structure they are supporting. We may use any and all types of invasive and non-invasive sensors, including but not limited to accelerometers, strain gauges, vibration sensors, displacement sensors, laser distance sensors, radar sensors, lidar sensors, infrared sensors, ultrasonic sensors, cameras, GPS sensors, pressure sensors, magnetic sensors, acoustic sensors, seismometers, and thermal sensors, to collect and analyze data as necessary for monitoring and evaluating the dynamics, behavior, and conditions of point targets, supporting structures, or pathways (such as roads) to which external point loads are applied. In the case of a camera, the camera detects in real-time the time-series displacement of visual target(s) on the structure being monitored. we have demonstrated the use of high-resolution optics attached to the camera, from which we extract raw data in real time via the image sensor to an external computing unit. This data is then processed and transformed without introducing any artificial artifacts, which is common in typical camera processing (since their goal is to produce visually appealing images, not accurate measurements). We have also developed our own tracking algorithm, specifically tailored for this application. We have also developed a custom tracking and detection algorithm that allows us to identify and track individual vehicle wheels, referred to as "point load," using just a single camera (though not exclusively). This system is effective even when the vehicle is traversing the structure being monitored, and not all wheels are visible within the camera's field of view. We also have a comprehensive list of inverse methods to determine the forces of individual point loads on the monitored structure, using time-series displacement data or the structure's dynamics under loading conditions. One of these methods, curve fitting, enables us to accurately determine the speed of each point load as it moves or is applied over time across the structure, with accuracy. For instance, when a vehicle crosses a bridge, we can determine its speed with greater accuracy than a laser speed meter by applying curve fitting techniques to the bridge's displacement data, which is associated with the travel of the vehicle across the bridge. Additionally, we have developed a system identification technique that eliminates the need for prior modeling or detailed knowledge of the structure's design. One of these methods consist of measuring the system impulse response or green function. Along the same lines as system identification, without explicitly knowing the blueprint or detailed information of the system, we have developed a more sophisticated approach based on a neural network methodology that works even if the system is nonlinear ─by linear, we mean that if a load is applied at a specific grid location on the structure and induces a displacement at the target, then if the same load is multiplied by a factor, the induced deflection will change by the same factor─ Basically, we developed everything in-house rather than simply integrating third-party solutions. We designed and built the entire system from the ground up, ensuring that every component, from the sensors to the algorithms, is specifically tailored to our unique requirements. This approach allows us to have full control over the performance and accuracy of the system, without relying on or patching together external solutions that may not meet our needs or introduce unnecessary limitations. Each time a vehicle, pedestrian, or any other external load traverses the monitored structure, without causing any disruption (such as interfering with traffic), and in the case of non-invasive sensors, without even making contact with the structure itself, we are able to collect the following information about the vehicle • Individual weight per wheel • Static weight of each wheel • Dynamic weight of each wheel (while in motion) • Weight distribution • Gross weight • Speed • Number of axles • Axle separation • Which axles are lifted and which are in contact with the ground • Department of Transportation (DOT) number (for U.S. and commercial vehicles) • Plate number • Vehicle size (length, width, height) • Acoustic profile associated with the vehicle • Noise level of the engine • Suspension details at each individual wheel • Information about the entire suspension system • Accurate speed • Center of gravity • All types of vehicle characteristics • Vehicle type (e.g., sedan, truck, SUV, bus, etc.) • Manufacturer information (e.g., make, model, year of manufacture) • Matching the car with internal or public databases to collect comprehensive data, including specifications, historical records, and any other relevant details specific to the vehicle.These information are disseminated in the web application. The same system could be used to detect the weight of the traversing vehicle and collect all relevant information as it moves, via a web app, allowing any authorized third party (such as the driver or the fleet owner in the case of commercial vehicles) to access this data without the need to stop and visit a scale, simply by accessing the web application. In the case of airplanes, this system could provide direct measurements of the aircraft's center of gravity as well as its weight, instead of relying on estimates or hearsay, as is currently the case. It can also enable airport authorities to directly assess an airplane’s weight, which is crucial for understanding the potential damage to airport pavements. Additionally, knowing the aircraft’s center of gravity is important for safety, as a heavier airplane or one with a center of gravity too far from its ideal position can pose significant risks during takeoff or landing The system could be used by law enforcement to either automatically issue tickets to overweight vehicles or as a screening tool to detect them for further inspection. It could flag vehicles that exceed legal weight limits, triggering automatic citations or alerts. Additionally, it could serve as a preliminary screening tool, flagging vehicles to be pulled over for detailed inspections at designated areas. The system would improve efficiency, reduce human error, and ensure consistent enforcement of weight regulations, ultimately enhancing road safety, reducing infrastructure damage, and saving resources. Particularly, this system could be used to deter overweight trucks on many grand regions and roads that are currently unmonitored or can't be easily monitored for weight law enforcement. The measurement conducted here is based on a fundamental physical quantity (i.e., displacement). Once the system is validated and adopted as a standard, it could be deployed on a large scale to conduct trade. Such a system, once validated as legal for trade, would be revolutionary, enabling freight quantities to be measured and traded in motion without the need to slow down. By knowing and tracking the volume of freight that each individual vehicle is transporting, as well as how these volumes change over time and across various trajectories, we can create a comprehensive freight movement and tracking model. This model can incorporate several key methods to optimize freight flow analysis. Origin-Destination (OD) Matrix Estimation can provide foundational insights by mapping volume changes between origin and destination pairs based on aggregate flow data, which allows for estimating probable paths and distribution patterns. Gravity Models enhance this by calculating the "attraction" between regions based on factors like economic size, distance, and demand, providing insights into inter- regional flow trends. Network Flow Models enable detailed route analysis using graph theory and optimization techniques like multi-commodity flow optimization, which helps in determining the most likely paths for freight based on constraints such as route capacity and costs. For situations where data is uncertain, Bayesian Inference Models can estimate freight movement using probabilistic updates, allowing the model to continuously learn and adapt based on incoming data. Additionally, Input- Output (IO) Analysis links freight volumes with production and consumption needs, making it possible to simulate flows based on economic demand in each region. Lastly, Spatial Interaction Models predict movement by evaluating regional interactions based on accessibility and socioeconomic factors. By integrating these approaches, the system can track and model freight movement dynamically and at scale, providing a highly detailed view of vehicle-level freight flows across the network. The system can be used for structural health monitoring through both temporal and frequency analysis simultaneously. It can detect changes in resonance frequencies, structural mode change, energy dissipation, resonance frequency linewidth, stiffness, phase shift, and other key indicators. Changes in energy dissipation allow us to detect alterations in the structure being monitored, as well as in its surrounding environment. For example, in the case of a bridge, this could indicate changes in the environment to which the bridge is connected. In the case of an airplane wing, this illustrates the connection between the wing and the main body of the aircraft as an example. This enables real-time structural health monitoring of the system, allowing for early detection as a warning system. In the case of non-invasive sensors, such as cameras, it can monitor the structure without requiring direct access. The system can also distinguish between changes in the structural behavior caused by variations in ambient environmental conditions and those resulting from actual structural changes. This capability extends the system's calibration lifespan when used for vehicle weighing measurements. By monitoring changes in the structural characteristics of a physical apparatus, it is possible to deduce changes in the mass of the object. We use this method to track fuel consumption even without direct access to the fuel storage system. Since fuel gets consumed, the mass of the physical apparatus storing the fuel changes. Also, we have shown that by just using camera and monitoring times series displacement of visual target(s) across the mechanical components of the power plant or other types of mechanical structures we could use to identify any mechanical anomalies. hat has the advantage of detecting an anomaly at an early stage, which is beneficial for safety. It helps prevent the anomaly from propagating, thus avoiding long shutdowns and repair times, while also mitigating risks. It also enables monitoring of moving mechanical parts or structures that cannot be easily instrumented or are inaccessible due to their movement, rotation, or location. Also, it is important to note that our approach to structural health assessments focuses on the critical preservation of measurement data integrity—a core principle that underpins our methodology. Unlike motion magnification algorithms and similar algorithms, which can distort data through excessive amplification and filtering, our method prioritizes accuracy without compromising integrity. This enables us to detect sudden changes that may occur over a short period of time—changes that these algorithms would not be able to identify. Conclusion This concludes the description of the preferred embodiment of the present invention. The foregoing description of one or more embodiments of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto.

Claims

WHAT IS CLAIMED IS 1. A computer implemented system comprising: (a) a computer having one or more memories; (b) one or more processors executing on the computer; (c) the one or more memories storing a set of instructions, wherein the set of instructions, when executed by the one or more processors cause the one or more processors to perform operations comprising: receiving obtaining sensor data comprising one or more displacements as a function of time of one or more targets attached to a structure in response to point loads applied to the structure; optionally receiving image data representing images of the vehicles comprising the point loads traversing the structure; determining, from the displacements, at least one of: a health status of the structure, or forces applied by one or more of the point loads by: obtaining a model for the displacements as a function of a forces applied by the point loads, wherein the model models the displacements as a superposition of responses of the structure to the one or more point loads at each of one or more coordinate locations in a virtual coordinate grid associated with or on the structure; and solving or deducing the model for the forces as an inverse problem using the coordinate locations of the point loads and the displacements obtained from the image data and the sensor data respectively.

2. The system of claim 1, wherein each of a plurality of individual cell in the grid are small enough to distinguish between the point loads comprising wheels of the vehicle.

3. The system of claim 1, wherein the operations comprise: determining the displacements as a function of time from the sensor data comprising images of the target comprising a visual target; obtaining an impulse response h(t) comprising components or coefficients at each coordinate location that are time dependent due to motion of the point loads and determining from the image data matched to the coordinate grid which coefficients or components are activated by application of the point load; and deducing or determining the forces or intensities of the point loads from the model relating the known displacements as a function of time to the intensities the known impulse response h(t) 4. The system of claim 1, wherein the model comprises a calibrated impulse response function of the structure comprising calibrated impulse response coefficients hxyat each of the coordinate locations x,y, the hxycoefficient relating a contribution to the displacements of one or more targets to the one or more point loads as they traverse the location x,y.

5. The system of claim 4, wherein the computer: receives the displacements comprising a time series of displacements over a measurement window or time segment, each of the displacements associated with a different time stamp; receives the image data representing a time series of images of the vehicles traversing the bridge; identifies the coordinate locations of the point loads of the vehicles at each of the time stamps; and determines the one or more forces at one or more of the coordinate locations using the calibrated response function.

6. The system of claim 3, wherein the solving comprises solving the model comprising a system of simultaneous linear equations in a matrix equation: D = A multiplied by W where matrix D contains the measurements of the displacement of the targets on the structure at each time instant in a measurement window or time segment as obtained from the sensor data; matrix W comprises a vector matrix^^^^2,.., ^^^^^^^^,.., ^^^^^^^^represent thedistinguishable point loads applied at the coordinate, ^^^^^^^^(^^^^))over thetime segment; and matrix A comprises the spatial-temporal values associated with each of the point loads applied during this time segment; wherein: ^^^^^^^^^^^^^^^^^^^^ ℎ(^^^^^^^^(^^^^), ^^^^^^^^(^^^^)) the impulse response coefficient associated with thecoordinate location (^^^^^^^^(^^^^), ^^^^^^^^(^^^^))then, the matrix A can be defined as:)so that ^^^^^^^^,^^^^represents the value in row t (time step) and column s (point load) in matrix A. and matrix A provides a temporal snapshot of each of the point loads ^^^^^^^^applied at a coordinate location over time as obtained from the image data; and the equation is solved to calculate the unknown forces comprising Wn given knowledge of A and D from the image data and sensor data respectively.

7. The system of claim 1, wherein the operations further include an object tracking algorithm that identifies a number and positioning of the point loads on each of the vehicles and tracks each of the point loads as the vehicles move across the structure during a measurement window with a unique identifier tag.

8. The system of claim 7, comprising the operations identifying the point loads comprising wheels associated with each of the vehicles that have entered a pre- selected region of interest in a field of view of a single camera observing the structure, by comparing spacings between the wheels to known spatial relationships in the image data, assuming the wheels on a common axle are perpendicular to the direction of travel of the vehicle, and wheels on one side of the vehicle are colinear with a direction of travel of the vehicle.

9. The computer system of claim 8, wherein the computer uses machine learning to identify the wheels.

10. The computer system of claim 1, wherein the model comprises curve fitting and the forces are fitting parameters to the curves used to fit the time series of the displacements.

11. The system of claim 1, further comprising: receiving the displacements comprising a time series of displacements over a measurement window or time segment, each of the displacements associated with a different time stamp; and the model comprising a neural network comprising: a plurality of inputs, each of the inputs for receiving an intensity of one of the forces applied by point loads at a different one of each of the coordinate locations of the point loads, a plurality of outputs, each of the outputs for outputting displacement of the targets measured at a given one of the time stamps in the measurement window, and one or more layers of interconnected nodes connecting the inputs to the outputs, wherein weighted connections between the nodes and activation functions at the nodes are determined through training with training data so that the layers accurately associate known ones of the intensities of the forces inputted at the inputs,through the weighted connections and the activation functions, to measured displacements at the outputs; and the computer operating the trained neural network in reverse working backward from the time series of displacements at the outputs to determine, as an inverse problem, the appropriate intensities at the inputs that are associated with the displacements.

12. The system of claim 1, further comprising monitoring changes in the displacements over time and associating abnormal changes in the displacements with a change in health status of the structure.

13. The system of claim 12, wherein the operation perform an analysis of the time series of the displacements in frequency domain and time domain (dynamic and transient) to determine at least one of resonance modes of the structure, a linewidth of the resonance modes, stiffness of the civil structure, or a phase shift of the time series of displacements.

14. The system of claim 12 or 13, wherein the operations: associate changes in the resonance modes or stiffness of the structure with structural changes in the structure and compares the changes with a model to determine if the changes correlate with those expected for environmental ambient changes, such as weather, or those expected for changes in a health status of the structure; and / or determines a linewidth of one or more peaks of the resonant modes and associates changes in the linewidth with changes in energy dissipation to an environment of the structure or structural damping changes.

15. The system of claim 14, wherein the structure comprises a bridge, a road, or a component of a power plant.

16. The computer system of claim 3 or 4, wherein the calibrated impulse response function coefficients are those that relate the time series of the displacements with known intensities of point loads at each of the coordinate locations.

17. The computer system of claim 16, wherein the calibrated response functions are updated to account for effects of weather or other environmental impacts on structural changes (mass, stiffness, resonance characteristics, damping) of the structure.

18. The computer system of claim 1, wherein the vehicle comprises at least one of a car, a truck, a train, an airplane, or one or more pedestrians and the structure comprises a bridge or a road.

19. The computer system of claim 18, wherein the target comprises a stain, catseye, roadmarker, a specialized layer of pavement applied to the road surface having a stiffness that enhances the displacement in response to passage of the point loads.

20. The computer system of claim 1, wherein the computing system learns to identify the targets comprising visual targets and deduce the time series displacement of the visual targets by tracking their location on each image frame of the images using machine learning.

21. The system of claim 20, wherein different types of object detection methods are utilized to determine the location of the same visual target , thereby assessing the error associated with the algorithm.

22. The system of claim 1 wherein the system automatically selects the target by utilizing pre-trained images of the target comprising typical visual features, such as stains, marks, and other characteristics commonly found on the structure.

23. The computing system of claim 1 using Super-Resolution Convolutional Neural Networks (SRCNNs) to improve the spatial resolution of the image data through advanced algorithmic super-resolution techniques to increase the spatial resolution of the measurement of the displacements.

24. A system for monitoring the structure of claim 1, further comprising at least of a sensor coupled to the structure for measuring the displacements or a camera coupled to the structure for capturing the images comprising the image data; and the computer system coupled to at least one of the sensor or the camera.

25. The system of claim 1 or 21, wherein the operations further comprise outputting an aggregation of the forces applied by the point loads, traffic information comprising a number of the vehicles, weather at the structure, health status of the structure, and lifetime of the structure.

26. A monitoring system, comprising: one or more sensors positioned for capturing electromagnetic signals or acoustic signals transmitted from a structure of a structure under test; and a computer system configured for: determining, from the signals, the displacement of one or more targets on the structure as a function of time; obtaining a model for the displacement as a function of load distribution on the structure, andsolving the model for the load distribution as an inverse problem using the displacement as a known data.

27. `The system of claim 26, wherein the structure is a component of a power plant.

28. The system of claim 26, wherein power plant comprises a turbine comprising a turbine shaft coupled to generator, and the signals are transmitted from a target located on the generator, the turbine; a case of the generator which is physically attached to the generator or the target at an interface between the turbine shaft and an entrance of the generator.

29. The system of claim 26 comprising a fuel gauge, wherein the structure is a wing on an aircraft or airplane and the computer determines, from the load distribution, a fuel level in a tank stored in the wing.

30. The system of claim 29, further comprising obtaining a power spectrum of the displacements wherein the model for the displacement comprises relating the power spectrum, comprising resonance modes of the wing, to the fuel level.

31. The system of claim 26 monitoring the structure comprising a wing / fuselage connection of an airplane.

32. The system of claim 1, further comprising the operations comprising: calculating dynamic and steady state components of the forces as the point loads comprising wheels traverse the structure;using the dynamic and steady state components to analyze behavior of the vehicle’s suspension system comprising individual wheel suspension systems; and deductively deriving a suspension characteristics of the vehicle by evaluating the responses of the individual wheel suspension system to the point loads.

33. A computer implemented method for determines the input loads applied to a structure comprising: analyzing, in the computer; displacement of target(s) on the structure, utilizing the structure’s impulse response, along with known trajectory of each of the input load, speed and acceleration of each of the loads along the trajectory, to obtain the input loads, where the displacement is a function of input location of each of the loads and is influenced by at least one of the point load’s speed or acceleration, or a combination of both.

34. The method of claim 33, wherein the impulse response is associated with a coordinate grid and the input loads are determined by reversing propagation through a neural network whose inputs comprise a vector that comprises multiple variables, including intensity of the load, speed of the load, acceleration of the load, and at least one of another characteristic of the load, or dynamic behavior of the bridge 35. The method of claim 33 or 34, where the system’s impulse response ateach grid location i,j is time dependent and comprises ℎ^^^^,^^^^(^^^^)36. The method of any of the claims 33-35, further comprising estimating the speed and acceleration from a traffic feed obtained using a camera and using the estimate as a baseline for further refinement of the speed and acceleration.

37. The system of any of the claims 1-36 wherein the operations further comprise calculating a center of gravity of the vehicle from the intensity, forces, or weight distribution of the point loads.

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