140. For the purpose of the disclosure, when referring to a longitudinal acceleration or a lateral acceleration of the tire 101, the longitudinal acceleration or the lateral acceleration may refer to an acceleration of the tire 101 itself and/or the vehicle on which the tire 101 is mounted. The data acquisition device 102 may comprise an onboard computing device 102 in communication with one or more distributed sensors and which is portable or otherwise modular as part of a distributed vehicle data collection and control system, or otherwise may be integrally provided with respect to a central vehicle data collection control system. The data acquisition device 102, or the onboard computing device 102, may include a processor 104 and a memory 106 having program logic 108 residing thereon, and in various embodiments may comprise a vehicle electronic control unit (ECU) or a component thereof, or otherwise may be discrete in nature, for example permanently or detachably provided with respect to a vehicle mount.

Generally stated, a system 100 as disclosed herein may implement numerous components distributed across one or more vehicles, for example but not necessarily associated with a fleet management entity, and further a central server network or event-driven serverless platform in functional communication with each of the vehicles via a communications network.

The illustrated embodiment of the system 100 may include for illustrative purposes, without otherwise limiting the scope of the present disclosure thereby, a tire-mounted sensor (TMS) unit 118 comprising at least one sensor 118 mounted on at least one of one or more tires 101 mounted on a vehicle, an ambient temperature sensor 112, a vehicle speed sensor 114 or a machine control sensor 114 configured to collect, for example, acceleration data associated with the vehicle or configured to detect one or more operating events of the vehicle, position sensors 116 such as global positioning system (GPS) transponders, and a DC power source 110. The tire mounted sensor unit 118 may include one or more sensors configured to generate output signals corresponding to tire conditions related to, or associated with, a motion of the one or more tires 101, or a motion of the vehicle on which the one or more tires 101 are mounted, including any or all of acceleration, such as longitudinal acceleration, lateral acceleration, or radial acceleration, velocity, angular velocity, tire deflection, tire strain, contained air temperature, inflation pressure, acoustic pressure, and the like, and such sensors may take any of various forms known to one of skill in the art for providing such signals. The at least one sensor 118 may be mounted on an inner liner, or some other structural component, of the at least one of the one or more tires 101 mounted on the vehicle. Various bus interfaces, protocols, and associated networks are well known in the art for the communication between the respective data sources and the local computing device 102 and/or the server 130, including for example an onboard receiver 122, and one of skill in the art would recognize a wide range of such tools and means for implementing the same.

In optional embodiments, data acquisition devices and equivalent data sources as disclosed herein, including the data acquisition device 102, are not necessarily limited to vehicle-specific sensors and/or gateway devices, and can also include third party entities and associated networks, program applications resident on a user computing device 140 such as a driver interface, a cloud-based data-management interface, a fleet management interface, and any enterprise devices or other providers of raw streams of logged data as may be considered relevant for algorithms and models as disclosed herein.

In some embodiments, one or more of the various sensors, including the ambient temperature sensor 112, the vehicle speed sensor 114, the position sensors 116, and the tire-mounted sensor unit 118, may be configured to communicate with downstream platforms without a local vehicle-mounted device or gateway components, such as for example via cellular communication networks or via a mobile computing device (not shown) carried by a user of the vehicle.

The term “user interface” as used herein may, unless otherwise stated, include any input-output module by which a user device facilitates user interaction with respect to a processing unit, server, device, or the like as disclosed herein including, but not limited to: downloaded or otherwise resident program applications; web browsers; web portals, such as individual web pages or those collectively defining a hosted website; and the like. A user interface may further be described with respect to a personal mobile computing device in the context of buttons and display portions which may be independently arranged or otherwise interrelated with respect to, for example, a touch screen, and may further include audio and/or visual input/output functionality even without explicit user interactivity. A user interface may additional be described with respect to a dashboard display housed within the interior of the vehicle in the context of buttons, knobs, and/or display portions that may be independently arranged or otherwise interrelated with respect to, for example, a touch screen, audio and/or visual input/output functionality, knobs or buttons configured to alter, for example, audio, radio frequencies, or air conditioning and/or heating, a dash instrument panel, or a heads-up display (HUD).

In optional embodiments, vehicle and tire sensors, including the ambient temperature sensor 112, the vehicle speed sensor 114, the position sensors 116, and the tire-mounted sensor unit 118, may further be provided with unique identifiers, wherein an onboard device processor can distinguish between signals provided from respective sensors on a same vehicle, and further in certain embodiments wherein a central processing unit and/or fleet maintenance supervisor client device may distinguish between signals provided from tires and associated vehicle and/or tire sensors across a plurality of vehicles. In other words, sensor output values may in various embodiments be associated with a particular tire, a particular vehicle, and/or a particular tire-vehicle system for the purposes of onboard or remote/downstream data storage and implementation for calculations as disclosed herein. An onboard data acquisition device 102 may communicate directly with the downstream processing stage 130, such as the remote server 130, as depicted in FIG. 1, or alternatively the user's mobile device or truck-mounted computing device may be configured to receive and process/transmit onboard device output data to one or more downstream processing units.

Raw signals received from at least one sensor mounted on at least one of one or more tires mounted on the vehicle 118, also referred to as to the tire-mounted sensor unit 118, as well as the ambient temperature sensor 112, the vehicle speed sensor 114, and the position sensors 116, may be stored in onboard device memory 106, or an equivalent local data storage network functionally linked to the onboard device processor 104, for selective retrieval and transmittal via a data pipeline stage as needed for calculations according to the method disclosed herein. A local or downstream “data storage network” as used herein may refer generally to individual, centralized, or distributed logical and/or physical entities configured to store data and enable selective retrieval of data therefrom, and may include for example, but without limitation, a memory, look-up tables, files, registers, databases, database services, and the like. In some embodiments, raw data signals from the various sensors, including the ambient temperature sensor 112, the vehicle speed sensor 114, the position sensors 116, and the tire-mounted sensor unit 118, may be communicated substantially in real time from the vehicle to a downstream processing unit such as the remote server 130. Alternatively, particularly in view of the inherent inefficiencies in continuous data transmission of high frequency data, the data may for example be compiled, encoded, and/or summarized for more efficient (e.g., periodic time-based or alternatively defined event-based) transmission from an onboard device (i.e., associated with the vehicle) to a remote processing unit via an appropriate (e.g., cellular) communications network.

Vehicle data and/or tire data, once transmitted via a communications network to a downstream processing unit, such as the remote server 130, or equivalent processing system, may be stored for example in a database 132 associated therewith and further processed or otherwise retrievable as inputs for processing via one or more algorithmic models 134 as disclosed herein. The models 134 may be implemented at least in part via execution of a processor, enabling selective retrieval of the vehicle data and/or tire data and further in electronic communication for the input of any additional data or algorithms from a database, lookup table, or the like that is stored in association with the processing unit.

Referring hereafter to FIG. 2, various embodiments of a method 200 may now be described for estimating a coefficient of friction for a surface 160 relative to the one or more tires 101 in contact with the surface 160, the one or more tires 101 mounted on the vehicle. Embodiments of a method 200 may comprise a testing stage and model generation stage associated with expected vehicle dynamics, as conveyed in steps 210-216, and a model implementation stage associated with actual vehicle dynamics, as conveyed in steps 220-260, or portions or variations thereof within the scope of the present disclosure. Otherwise stated, models as disclosed herein may initially be generated and subsequently implemented and/or modified by a given entity, or an entity may merely selectively retrieve one or more models for implementation that have been generated by another.

In accordance with the method 200, and referring to the testing and model generation stage associated with the expected vehicle dynamics, as depicted in step 210, various inputs set forth in step 212 are provided for data processing and a generation of one or more models, as depicted in step 214, specific to the one or more tires 101 being tested. At least one surface condition, as depicted by step 216, may be associated, or at least commonly associated with, each of the one or more models, the one or more models of which may be linear or non-linear. In optional embodiments, as illustratively conveyed in FIGS. 3-4D, the various inputs may be collected through offline or online testing, wherein the various inputs in the generation of the one or more models may comprise at least an expected motion of the at least one of the one or more tires 101 mounted on the vehicle related to at least one of the one or more operating events on the at least one of the one or more tires mounted on the vehicle. In optional embodiments, the one or more operating events, as conveyed in the step 212, may include at least one of an acceleration of the at least one of the one or more tires 101 mounted on the vehicle, an acceleration of the vehicle on which the one or more tires 101 are mounted, a deceleration of the at least one of the one or more tires 101 mounted on the vehicle, a deceleration of the vehicle on which the one or more tires 101 are mounted, a steering of the at least one of the one or more tires mounted 101 on the vehicle, or a steering of the vehicle on which the one or more tires 101 are mounted, and combinations thereof.

In other optional embodiments, and referring to FIG. 3, wherein an x-y-z coordinate system in relation to at least one of the one or more tires 101 is illustratively conveyed, the expected motion of the at least one of the one or more tires 101 mounted on the vehicle, or the vehicle on which the at least one of the one or more tires 101 are mounted, may include: a lateral acceleration of the at least one of the one or more tires 101 corresponding to a force exerted in a y-direction (F_y) 152 on the at least one of the one or more tires 101, or a rotation 153, or a pitch 153, about the force exerted in the y-direction (F_y) 152 on the at least one of the one or more tires 101; a lateral acceleration of the vehicle on which the at least one of the one or more tires 101 are mounted; a longitudinal acceleration of the at least one of the one or more tires 101 corresponding to a force exerted in an x-direction (F_x) 150 on the at least one of the one or more tires 101, or a rotation 151, or a roll 151, about the force exerted in an x-direction (F_x) 150 on the at least one of the one or more tires 101; a longitudinal acceleration of the vehicle on which the at least one of the one or more tires 101 are mounted; a vertical acceleration of the at least one of the one or more tires 101 corresponding to a normal force exerted in a z-direction (F_z) 154, or a rotation 155, or a yaw 155, about the normal force exerted in the z-direction (F_z) 154; or a radial acceleration of the at least one of the one or more tires 101 corresponding to an angular velocity (ω) 156. Additional inputs or data corresponding to a saturation point, a footprint length (FPL), or a torque (τ) may be received from the tire-mounted sensor unit 118, or from other sensors, including the vehicle speed sensor 114 or the position sensors 116, either as a direct input or calculated based on other inputs such as the lateral acceleration, the longitudinal acceleration, the vertical acceleration, or the radial acceleration. For the purpose of the disclosure, the expected motion of the at least one of the one or more tires 101 mounted on the vehicle, or the vehicle on which the at least one of the one or more tires 101 are mounted, may include (without limitation) any or all of acceleration, such as longitudinal acceleration, lateral acceleration, or radial acceleration, velocity, angular velocity, tire deflection, tire strain, contained air temperature, inflation pressure, acoustic pressure, and the like.

Referring to FIGS. 2 and 4A-4D, the testing and model generation stage associated with the expected vehicle dynamics of the method 200, as depicted in the step 210, may comprise the generation of one or more models, as depicted in the step 214, specific to the one or more tires 101 being tested. As depicted in FIGS. 4A-4D, a non-linear relationship may be identified between the various inputs received from the vehicle and tire sensors, such as the tire-mounted sensor unit 118. Data underlying the generation of the one or more models, as depicted in the step 214, may be used to create an algorithm. With this algorithm, a relationship may be identified between at least the expected motion and the one or more operating events of the at least one of the one or more tires 101 mounted on the vehicle. In optional embodiments, the generation of the one or more models may be implemented substantially in real time based on actual inputs during operation of the at least one of the one or more tires 101 on the vehicle.

Referring to FIG. 2, with respect to the generation of the one or more models, as depicted in the step 214, and a creation of the algorithm from data underlying the various inputs received from vehicle and tire sensor, the at least one surface condition may be associated, or at least commonly associated with, each of the one or more models, as depicted in the step 216. In optional embodiments, the at least one surface condition may include a surface condition corresponding to a type or a material of the surface 160, including (without limitation) asphalt, concrete, rock (or some other mineral), grass, mud, or dirt, or the at least one surface condition may include a surface condition corresponding to an external factor affecting or impacting the type or the material of the surface 160, including moisture or water, whether due to rainfall or otherwise, iciness, whether due to snow, sleet, or otherwise, or another external factor. In other optional embodiments, the at least one surface condition may include values of a coefficient of friction (μ), including actual, expected values of the coefficient of friction or general categorizations of the expected values of the coefficient of friction, such as a “high,” “medium,” or “low” coefficient of friction.

Referring to FIGS. 2 and 4A-4D, the method 200 may include the model implementation stage associated with the actual vehicle dynamics, as conveyed in step 220. As depicted in step 222, various inputs, including the one or more operating events on the at least one of the one or more tires 101 mounted on the vehicle, may be detected by the tire-mounted sensor unit 118, or from other sensors, including the vehicle speed sensor 114 or the position sensors 116. As further depicted in the step 222, for at least one of the one or more operating events, at least signals representative of a sensed motion may be received by the tire-mounted sensor unit 118—the at least one sensor mounted on the at least one of the one or more tires mounted on the vehicle 118—or from other sensors, including the vehicle sensor 114 or the position sensors 116. In optional embodiments, and as previously disclosed within the context of the step 212, the one or more operating events, as conveyed in step 222, may include at least one of an acceleration of the at least one of the one or more tires 101 mounted on the vehicle, an acceleration of the vehicle on which the at least one of the one or more tires 101 are mounted, a deceleration of the at least one of the one or more tires 101 mounted on the vehicle, a deceleration of the vehicle on which the at least one of the one or more tires 101 are mounted, a steering of the at least one of the one or more tires mounted 101 on the vehicle, or a steering of the vehicle on which the at least one of the one or more tires 101 are mounted, and combinations thereof.

In other optional embodiments, and referring to FIGS. 2-3, wherein an x-y-z coordinate system in relation to at least one of the one or more tires 101 is illustratively conveyed, the sensed motion of the at least one of the one or more tires 101 mounted on the vehicle, or the vehicle on which the at least one of the one or more tires 101 are mounted, may include: a sensed lateral acceleration of the at least one of the one or more tires corresponding to the force exerted in a y-direction (F_y) 152 on the at least one of the one or more tires 101, or the rotation 153, or the pitch 153, about the force exerted in the y-direction (F_y) 152 on the at least one of the one or more tires 101; a sensed lateral acceleration of the vehicle on which the at least one of the one or more tires 101 are mounted; a sensed longitudinal acceleration of the at least one of the one or more tires 101 corresponding to a force exerted in an x-direction (F_x) 150 on the at least one of the one or more tires 101, or the rotation 151, or the roll 151, about the force exerted in an x-direction (F_x) 150 on the at least one of the one or more tires 101; a sensed longitudinal acceleration of the vehicle on which the at least one of the one or more tires 101 are mounted; a sensed vertical acceleration of the at least one of the one or more tires 101 corresponding to a normal force exerted in a z-direction (F_z) 154, or the rotation 155, or the yaw 155, about the normal force exerted in the z-direction (F_z) 154; or a sensed radial acceleration of the at least one of the one or more tires 101 corresponding to an angular velocity (ω) 156. For the purpose of the disclosure, the sensed motion of the at least one of the one or more tires 101 mounted on the vehicle, or the vehicle on which the at least one of the one or more tires 101 are mounted, may include (without limitation) any or all of acceleration, such as longitudinal acceleration, lateral acceleration, or radial acceleration, velocity, angular velocity, tire deflection, tire strain, contained air temperature, inflation pressure, acoustic pressure, and the like.

In further optional embodiments, additional inputs corresponding to the saturation point, the footprint length (FPL), or the torque (τ) may be received, directly or indirectly, from the tire-mounted sensor unit 118, or from other sensors, including the vehicle speed sensor 114 or the position sensors 116. A computing device, whether the onboard data acquisition device 102, the remote server 130, or the user computing device 140, which is communicatively linked to the tire-mounted sensor unit 118, or other sensors, such as the vehicle speed sensor 114 or the position sensors 116, may be configured to determine the saturation point of the at the at least one of the one or more tires 101 mounted on the vehicle based at least in part on the at least signals representative of the sensed motion, as depicted in step 226. “Saturation” is defined as a deficiency or inability of the at least one of the one or more tires 101 to generate an increasing force in a linear manner across either the force exerted in the y-direction (F_y) 152—the lateral direction—or the force exerted in the x-direction (F_x) 150—the longitudinal direction.

In yet further optional embodiments, the computing device, whether the onboard data acquisition device 102, the remote server 130, or the user computing device 140, which is communicatively linked to the tire-mounted sensor unit 118, or other sensors, such as the vehicle speed sensor 114 or the position sensors 116, may be configured to calculate a torque (τ) from the at least one of the one or more tires 101 mounted on the vehicle based at least in part on the at least signals representative of the sensed motion, as depicted in step 224. The computing device may determine the saturation point of the at least one of the one or more tires 101 mounted on the vehicle based at least in part on the calculated torque, as depicted in the step 226.

In certain embodiments, the footprint length (FPL), the saturation point, or the torque (τ) may be collected or calculated directly or indirectly from the tire-mounted sensor unit 118, or from other sensors, including the vehicle speed sensor 114 or the position sensors 116, and combinations thereof, or the footprint length (FPL), the saturation point, or the torque (τ) may be calculated or determined directly or indirectly by the computing device connected to the various foregoing sensors. In one embodiment, data corresponding to an acceleration waveform of the at least one of the one or more tires 101 may be collected in a radial direction, such as the radial acceleration of the at least one of the one or more tires 101 corresponding to the angular velocity (ω) 156, from sampled outputs of the at least one sensor mounted on the at least one of the one or more tires 101 mounted on the vehicle. The acceleration waveform may then be integrated in the tire radial direction to generate a velocity waveform, wherein a number of samples during ground contact are calculated from at least first and second peaks in the velocity waveform. With respect to footprint length, from a physical understanding of the velocity (integrated acceleration) profile, one of skill in the art may appreciate that the entrance and exit of the ground contact patch (footprint) are identifiable as corresponding with a difference in a number of samples between first and second waveform peaks of the integrated accelerometer signal, accordingly corresponding with the number of samples taken in a footprint area.

Referring to FIG. 2, the model implementation stage associated with the actual vehicle dynamics of the method 200 may continue with a step 230, wherein the one or more models, as depicted in the step 214, are selectively retrieved. Selective retrieval of the one or more models may be performed by a user-initiated event or through an automatic, non-manual event. At least one surface condition, as set forth in the step 216, may be associated, or at least be commonly associated, with each of the one or more models. The model implementation stage associated with the actual vehicle dynamics of the method 200 may further continue with an estimation of respective values corresponding to a coefficient of friction of the surface 160 relative to the one or more tires 101 in contact with the surface 160, as depicted in step 240. The computing device, whether the onboard data acquisition device 102, the remote server 130, or the user computing device 140, may estimate the respective values corresponding to the coefficient of friction of the surface 160 relative to the one or more tires 101 in contact with the surface 160 based on at least the one or more models, the at least one of the one or more operating events, and the sensed motion.

Referring to FIGS. 2 and 4A, graphical diagrams representing one or more operating events on and an acceleration of the at least one of the one or more tires 101 mounted on the vehicle is depicted. In the graphical diagrams of FIG. 4A, the one or more operating events may comprise a braking input on, or a deceleration of, the at least one of the one or more tires 101 mounted on the vehicle, or a steering input on the at least one of the one or more tires 101 mounted on the vehicle. When the at least one of the one or more operating events, such as the braking input or the steering input, is measured against the sensed motion including the sensed acceleration, such as the sensed longitudinal acceleration or the sensed lateral acceleration, of the at least one of the one or more tires 101 mounted on the vehicle, at least one surface condition corresponding to a value of a coefficient of friction, such as a “high” or “low” coefficient of friction, may be ascertained with respect to a maximum value of the acceleration when the at least one of the one or more tires 101 has achieved a point of saturation. Specifically in the step 240, the method 200 may continue with the estimation of the respective values corresponding to the coefficient of friction of the surface 160 relative to the one or more tires 101 in contact with the surface 160 based on at least the one or more non-linear models, the at least one of the one or more operating events, and a maximum value of the sensed acceleration corresponding to the determined saturation point, as depicted in the step 226. As depicted in FIG. 4A, the maximum value of the sensed acceleration, such as the sensed lateral acceleration or the sensed longitudinal acceleration, corresponding to the determined saturation point is evidenced by a horizontal dashed line having a slope value of approximately, or at, zero. The graphical diagram of FIG. 4A conveys simplified curves representing a generally mean line of data corresponding to the sensed acceleration across the at least one of the one or more operating events.

Referring to FIGS. 2 and 4B, graphical diagrams representing one or more operating events on and an acceleration of the at least one of the one or more tires 101 mounted on the vehicle is depicted. In the graphical diagrams of FIG. 4B, the one or more operating events may comprise a braking input on, or a deceleration of, the at least one of the one or more tires 101 mounted on the vehicle, or a steering input on the at least one of the one or more tires 101 mounted on the vehicle. When the at least one of the one or more operating events, such as the braking input or the steering input, is measured against the sensed motion including the sensed acceleration, such as the sensed longitudinal acceleration or the sensed lateral acceleration, or the yaw about the normal force exerted on the at least one of the one or more tires 101 mounted on the vehicle, at least one surface condition corresponding to a value of a coefficient of friction, such as a “high” or “low” coefficient of friction, may be ascertained with respect to a change of rate of acceleration preceding the point of saturation for the at least one of the one or more tires 101 mounted on the vehicle. Specifically, in the step 240, the method 200 may continue with the estimation of the respective values corresponding to the coefficient of friction of the surface 160 relative to the one or more tires 101 in contact with the surface 160 based on at least the one or more non-linear models, the at least one of the one or more operating events, and a change of rate of the sensed acceleration preceding the determined saturated point, as depicted in the step 226. As depicted in FIG. 4B, the change of rate of the sensed acceleration, such as the sensed longitudinal acceleration or the sensed lateral acceleration, or the yaw about the normal force exerted on the at least one of the one or more tires 101, preceding the determined saturation point is evidenced by a dashed line having a slope value of greater than zero. The graphical diagrams of FIG. 4B conveys simplified curves representing a generally mean line of data corresponding to the sensed acceleration across the at least one of the one or more operating events.

Referring to FIGS. 2 and 4C, a graphical diagram representing one or more operating events on and an acceleration of the at least one of the one or more tires 101 mounted on the vehicle is depicted. In the graphical diagram of FIG. 4C, the one or more operating events may comprise a steering input on the at least one of the one or more tires 101 mounted on the vehicle. When the at least one of the one or more operating events, such as the steering input, is measured against a values of torque (τ) calculated from the sensed motion, including the sensed acceleration, of the at least one of the one or more tires 101 mounted on the vehicle, at least one surface condition corresponding to a value of a coefficient of friction, such as a “high” or “low” coefficient of friction, may be ascertained with respect to a change of rate of the calculated torque preceding the point of saturation for the at least one of the one or more tires 101 mounted on the vehicle. Specifically, in the step 240, the method may continue with the estimation of the respective values corresponding to the coefficient of friction of the surface 160 relative to the one or more tires 101 in contact with the surface 160 based on at least the one or more non-linear models, the at least one of the one or more operating events, and a change of rate of the calculated torque preceding the determined saturated point, as depicted in the step 224 and the step 226. As depicted in FIG. 4C, the change of rate of the calculated torque preceding the determined saturation point is evidenced by a dashed line having a slope value of greater than zero. The graphical diagram of FIG. 4C conveys simplified curves representing a generally mean line of data corresponding to the calculated torque across the at least one of the one or more operating events.

Referring to FIGS. 2 and 4D, graphical diagrams representing one or more operating events on and an acceleration of the at least one of the one or more tires 101 mounted on the vehicle is depicted. In the graphical diagrams of FIG. 4D, when the at least one of the one or more operating events, such as the steering input or braking input, is measured against the sensed motion, including the sensed acceleration, of the at least one of the one or more tires 101 mounted on the vehicle, at least one surface condition corresponding to a type or a material of the surface 160, such as concrete, or at least one surface condition corresponding to an external factor, such as iciness, may be ascertained with respect to a trailing edge and a leading edge of the at least one of the one or more tires 101 mounted on the vehicle, commonly associated with a footprint length (FPL) or contact patch of the at least one of the one or more tires 101. In the graphical diagram of FIG. 4D, the sensed acceleration of the at least one of the one or more tires 101 may constitute the radial acceleration of the at least one of the one or more tires 101 corresponding to the angular velocity (ω) 156. Specifically, in the step 240, the method 200 may continue with the estimation of the respective values corresponding to the coefficient of friction of the surface 160 relative to the one or more tires 101 in contact with the surface 160 based on at least the one or more non-linear models, the at least one of the one or more operating events, and a footprint length (FPL) calculated from the radial acceleration of the at least one of the one or more tires 101. The graphical diagrams of FIG. 4D conveys simplified curves representing a generally mean line of data corresponding to the radial acceleration of the at least one or more tires 101 due from the at least one of the one or more operating events.

Referring to FIG. 2, in optional embodiments, the model implementation stage associated with the actual vehicle dynamics of the method 200 may continue with a step 242. The estimated respective values corresponding to the coefficient of friction of the surface 160 relative to the one or more tires 101 in contact with the surface 160 may be used as an input for a tire traction model, as depicted in the step 242. A tire wear status (e.g., tread depth) may for example be provided along with the above-referenced estimated coefficient of friction as inputs to a tire traction model, which may be configured to provide an estimated traction status or one or more traction characteristics for the respective tire. As with the aforementioned wear model, the traction model may comprise “digital twin” virtual representations of physical parts, processes, or systems wherein digital and physical data are paired and combined with learning systems such as for example artificial neural networks. Real vehicle data and/or tire data from a particular tire, vehicle or tire-vehicle system may be provided throughout the life cycle of the respective asset to generate a virtual representation of the vehicle tire for estimation of tire traction, wherein subsequent comparison of the estimated tire traction with a corresponding measured or determined actual tire traction may preferably be implemented as feedback for machine learning algorithms executed at a server level. The tire traction model may in various embodiments utilize the results from prior testing, including for example stopping distance testing results, tire traction testing results, etc., as collected with respect to numerous tire-vehicle systems and associated combinations of values for input parameters (e.g., tire tread, inflation pressure, surface characteristics, vehicle acceleration, slip rate and angle, normal force, braking pressure and load), wherein a tire traction output may be effectively predicted for a given set of current vehicle data and tire data inputs.

In other optional embodiments, the method 200 may also involve providing inputs such as the estimated forces acting on the at least one of the one or more tires 101 or the estimated respective values corresponding to the coefficient of friction, alone or in combination with other relevant metrics, as inputs to a tire durability and health model. Such a model may be implemented for estimating relative fatigue characteristics, for example as an indicator of durability events such as tread/belt separations. Such a model may also for example be implemented for estimating relative tire aging characteristics or predicting wear state at one or more future points in time. Feedback signals corresponding to such durability events may be provided via an interface to the data acquisition device 102 associated with the vehicle itself, or to user computing device 140, such as for example integrating with a user interface configured to provide alerts or notice/recommendations of an intervention event, such as for example that one or more tires should or soon will need to be replaced, rotated, aligned, inflated, and the like. Outputs from a tire durability and health model may further or in the alternative be provided to the traction model referenced above.

Referring to FIG. 2, the model implementation stage associated with the actual vehicle dynamics of the method 200 may continue with a step 250 wherein an output signal corresponding to the estimated respective values corresponding to the coefficient of friction of the surface 160 relative to the one or more tires 101 in contact with the surface 160 is generated. In optional embodiments, the output signal may be provided to a user interface associated with the vehicle for local display to a user of the vehicle, as depicted in step 252, and/or a user interface associated with a remote computing device via, for example, a cloud-based data-management platform, such as a fleet management telematics platform, as depicted in step