JOINT OPTIMIZATION OF ROUTES AND DRIVING PARAMETERS FOR CYCLE DEGRADATION MINIMIZATION IN ELECTRIC VEHICLES TECHNICAL FIELD [0001] The present disclosure relates to a method for estimating an impact of a selected route on a state of health, SoH, of a battery in a heavy-duty electric vehicle, for example, in a vehicle with an electric battery powered propulsion system and to various related aspects. [0002] In particular, but not exclusively, the disclosed technology uses a battery degradation model which models how discharging affects the state of health of a battery. The state of health of a battery may also be affected by factors such as braking where this creates regenerative charge. [0003] This is particularly useful for vehicles which have an electric propulsion system, so called electric vehicles. Electric vehicles may be manually operated or driven, but may also be autonomous or semi-autonomous or remotely operated or driven. The disclosed invention will be described mainly with respect to electric vehicles, however, such electric vehicles may include heavy-duty electric vehicles, such as semi-trailer vehicles and trucks as well as other types of vehicles such as cars. BACKGROUND [0004] Electric vehicles are becoming more common and will soon be the norm in terms of road transportation, which justifies the interest of researches in topics related to health management and exploitation of such vehicles. So far, however, electric vehicle management emphasizes charging strategies and routing optimization, mainly focused on energy consumption and no investigation has been performed on the impact that routing and driving parameters, such as maximum speed and acceleration, have on the useful life of a battery and therefore on the long term exploitation cost of a fleet of electric vehicles. [0005] To deal with the climate change consequences, several global actors have announced efforts to reduce emissions. For example, through the communication of the European Green Deal (EGD) REF, Europe announces, among other things, the intention to reach a zero net emission of greenhouse gases by 2050. This will impact the automotive sector and the number of Electric vehicles (EV’s) will become immense, according to the EGD ”by 2025, about 1 million public recharging and refuelling stations will be needed for the 13 million zero - and low-emission vehicles expected on European roads”. It also highlights the importance of ensuring ”a safe, circular and sustainable battery value chain for all batteries”. With different countries and global actors adopting similar stances, it is natural that research on health management for vehicles and batteries have become such important topics within the literature. However, the relationship between routing, vehicle exploitation and degradation is not well explored even for conventional vehicles. [0006] For example, Robert et al. (2019) describes where missions and maintenance operations are scheduled for a fleet of trucks without considering routing details and Jbili et al. (2018) describes an approach where the routing is considered. In both of those works, the vehicle is treated as a single component system with non-negligible, in other words, with non-neglectable, failure probabilities that must be, in some sense, minimized. Xu et al. (2018) describes how some of the main stress factors such as Depth of discharge (DoD) and mean state of charge (mSoC) can be correlated to vehicle routes and exploitation. [0007] The disclosed technology seeks to mitigate, obviate, alleviate, or eliminate various issues known in the art which affect the state of health of a battery, such as, for example, those mentioned above. SUMMARY [0008] Whilst the invention is defined by the accompanying claims, various aspects of the disclosed technology including the claimed technology are set out in this summary section with examples of some preferred embodiments and indications of possible technical benefits. [0009] Since failures tend to happen rarely in the lifetime of a vehicle, even an electric vehicle, many of the methods disclosed in the prior art are not applicable for most of the useful life of a vehicle where failure probabilities are sufficiently low to be ignored and so are not adaptable for reducing the long-term exploitation cost. For EV’s in particular, the relationship between routes, driving parameters and degradation can be impactful in terms of battery end of life. [00010] Some embodiments of the disclosed technology accordingly comprise a method for estimating battery degradation based on routes and driving parameters; integrating the estimated battery degradation in a decision making optimization problem to find the best route, maximum speed and acceleration in terms of energy consumption, degradation and delay; and validating the optimization through simulations which assess the impact that randomness of real traffic conditions can have on battery degradation. [00011] Advantageously, by exploring the link between the main stress factors such a DoD and mSOC and vehicle routes and exploitation, the disclosed technology may lead to optimization of vehicle usage, improvement of useful life of batteries and even tools for better dimensioning maintenance contracts in the future. [00012] Whilst the invention is defined by the accompanying claims, various aspects of the disclosed technology including the claimed technology are set out in this summary section with examples of some preferred embodiments and indications of possible technical benefits. [00013] The disclosed technology relates to a deterministic method to estimate the impact of a route in the state of health of a battery. This method is used to optimize routes while respecting operational constraints, such as delay penalties, and the impacts of such optimization on the long-term cost are estimated through simulations, mimicking real driving conditions and traffic randomness. [00014] A first aspect of the disclosed technology relates to a method, for example a computer implemented method, for estimating an impact of a selected route on a state of health, SoH, of a battery in a heavy-duty vehicle, such as a truck or semi-trailer, the method comprises predicting a required power profile for a given route at least partly based on a road topology of the route, configuring a dynamic battery model, and feeding the predicted power profile to the dynamic battery model, thereby obtaining a predicted state of charge, SoC, profile for the given route, and configuring a degradation model for the battery of the heavy-duty vehicle (100), and feeding the predicted SoC profile of the route to the degradation model, thereby obtaining the impact of the selected route on the SoH of the battery. [00015] Advantageously, the method allows a more realistic prediction of how a battery may degrade based on particular routes a vehicle follows. [00016] In some embodiments, wherein the selected route comprises a set of points in space to visit, with known addresses. [00017] In some embodiments, the selected route is associated with information related to vehicle speed and/or vehicle acceleration. [00018] In some embodiments, the required power profile is based on a required mechanical power of the selected route and on an efficiency of a power train of the heavy- duty vehicle. [00019] In some embodiments, the required power profile is based on an efficiency of a power train of the heavy-duty vehicle. [00020] In some embodiments, the dynamic battery model combines a Kinetic Battery Model, kiBam, with a second order equivalent circuit model, ECM. [00021] In some embodiments, the dynamic battery model comprises instead of the Kibam and ECM, a Coulomb counting model and an equivalent circuit model. [00022] In some embodiments, battery degradation is defined in terms of a capacity degradation of the battery. [00023] In some embodiments, the degradation model for the battery determines degradation whilst the battery is discharging. [00024] In some embodiments the degradation model for the battery determines degradation whilst the battery is both discharging and charging. [00025] In some embodiments, the SoC profile of the route accounts for one or more interactions of the vehicle with one or more other vehicles along the route. [00026] In some embodiments, the degradation model for the battery determines degradation whilst the battery is regeneratively charging. [00027] Advantageously, in some embodiments, the disclosed dynamic battery model is used to configure the battery degradation model to model not just degradation whilst discharging, but also whilst the vehicle is driving by modelling how the battery degrades as the battery is charging and as the battery is discharging to be modelled, for example, the degradation of the battery may modelled as the battery undergoes regenerative charging, for example, as the vehicle brakes due to interactions with other vehicles and/or traffic lights. [00028] According to another aspect of the disclosed technology, a method, for example a computer implemented method, for selecting a route for a heavy-duty vehicle, comprises identifying a set of candidate routes, configuring a cost function comprising a state of health, SoH, evolution (Cdeg) of a battery on the heavy-duty vehicle, evaluating each route in the set of routes according to the configured cost function, and selecting the route based on the evaluation. [00029] Advantageously, the method for selecting a route for a heavy-duty vehicle allows the selection of routes to optimize long term health of the battery used by the heavy- duty vehicle in terms of its ability to retain charge and/or its charge capacity over a number of charging cycles. [00030] In some embodiments, the cost function comprises an energy consumption cost (C _energy ) and/or a cost associated with route delay (C _delay ). [00031] In some embodiments, the cost function is configured for a SoH of a battery using a battery degradation model which determines degradation whilst the battery is discharging and charging. [00032] In some embodiments, the SoH of the battery is based on a SoC profile of the battery for each route in the set of candidate routes which accounts for one or more interactions of the vehicle with one or more other vehicles along that candidate route. [00033] In some embodiments, the degradation model for the battery determines degradation whilst the battery is regeneratively charging, for example, due to the vehicle braking due to interactions with other vehicles and/or traffic lights etc. [00034] In some embodiments, the state of health evolution of the cost function is determined using a method according to the first aspect or any one of its disclosed embodiments to estimate the impact of each candidate route on the state of health of the battery of the heavy-duty vehicle. [00035] In some embodiments where the method of route selection uses the method according to the first aspect which includes modelling the degradation of the battery, the modelling of the degradation of the battery also includes a traffic model for interactions with other vehicles to model how the battery changes speed and accelerates along the route. In some embodiments, how the battery regeneratively charged, for example, as the vehicle brakes due to an interaction with another vehicle is also modelled. [00036] According to another aspect of the disclosed technology, a method, for example a computer implemented method, for estimating battery degradation in a heavy- duty vehicle such as a truck or semi-trailer, based on candidate routes and driving parameters, comprising integrating a decision making optimization problem that finds the best route, maximum speed and acceleration in terms of energy consumption, degradation and delay. [00037] Advantageously, the method may be used to manage battery health so that the life-time of the battery in terms of its capacity to retain charge is optimized. [00038] In some embodiments, the method for estimating battery degradation in a heavy duty vehicle comprises obtaining one or more candidates routes and driving parameters, generating a decision making optimization problem, and finding as a solution to the optimization problem, one or more or all of: a best route for the vehicle to follow, a maximum speed of the vehicle, and a maximum acceleration of the vehicle. [00039] In some embodiments, the optimization problem comprises finding a solution to a cost function for a state of health evolution of a battery of the heavy-duty vehicle (100) based on a power profile for the vehicle indicating an energy consumption of the vehicle along a route, a battery degradation model for the battery of the vehicle, and a route delay cost function. [00040] In some embodiments, the solution to the for the state of heath evolution using a method according to the first aspect or any one of its embodiments disclosed herein to estimate the impact of each candidate route on the state of health of the battery of the heavy-duty vehicle. [00041] In some embodiments, the method further comprises predicting a point in time when the battery degradation is estimated to meet a condition for a battery replacement alert to be generated. For example, when the battery has degraded past a threshold charge capacity. [00042] Another aspect of the disclosed technology comprises an apparatus comprising memory, one or more processors or processing circuitry, and computer program code, wherein when the computer program code is loaded from memory and executed by the one or more processors, the apparatus is configured to perform a method according to one or more or all of the above method aspects or an embodiment thereof disclosed herein. [00043] In some embodiments, the apparatus is one of a heavy-duty vehicles, a component or sub-system of the heavy-duty vehicle, and a server configured to wirelessly communicate with the heavy-duty vehicle, such as for example, a back-office server for a vehicle fleet if the vehicle is a member of the fleet. [00044] Another aspect of the disclosed technology comprises a computer program product comprising computer-code which when loaded from memory and executed by one or more processors of a control circuit of a vehicle having an automated driving system, causes the vehicle to implement a method according to one or more or all of the above method aspects or an embodiment thereof disclosed herein. [00045] Another aspect of the invention comprises a computer-readable storage medium comprising computer-program code which, when executed by one or more processors or processing circuitry of an apparatus, causes the apparatus to implement a method according to the first aspect or any of its embodiments disclosed herein. [00046] Another aspect of the disclosed technology relates to a computer program comprising computer code comprising one or more modules or means for performing an aspect of the method of estimating an impact of a selected route on a state of health, SoH, of a battery in a heavy-duty vehicle according to the first aspect or any of its embodiments disclosed herein, when said program is run on one or more processors or on processing circuitry of a control unit. [00047] Another aspect of the disclosed technology relates to a computer program comprising computer code comprising one or more modules or means for performing an aspect of the method for selecting a route for a heavy-duty vehicle or any of its embodiments disclosed herein, when said program is run on one or more processors or on processing circuitry of a control unit. [00048] Another aspect of the disclosed technology relates to a computer program comprising computer code comprising one or more modules or means for performing an aspect of the method for estimating battery degradation in a heavy-duty vehicle for or any of its embodiments disclosed herein, when said program is run on one or more processors or on processing circuitry of a control unit. [00049] Another aspect of the disclosed technology comprises a computer program carrier carrying a computer program comprising computer-program code according to the above aspects, which, when loaded from the computer program carrier and executed by one or more processors or processing circuitry of an apparatus causes the apparatus to implement an aspect of the method of estimating an impact of a selected route on a state of health, SoH, of a battery in a heavy-duty vehicle or an embodiment thereof disclosed herein, wherein the computer program carrier is one of an electronic signal, optical signal, radio signal or computer-readable storage medium. [00050] Another aspect of the disclosed technology comprises a computer program carrier carrying a computer program comprising computer-program code according to the above aspects, which, when loaded from the computer program carrier and executed by one or more processors or processing circuitry of an apparatus causes the apparatus to implement an aspect of the method for selecting a route for a heavy-duty vehicle or an embodiment thereof disclosed herein, wherein the computer program carrier is one of an electronic signal, optical signal, radio signal or computer-readable storage medium. [00051] Another aspect of the disclosed technology comprises a computer program carrier carrying a computer program comprising computer-program code according to the above aspects, which, when loaded from the computer program carrier and executed by one or more processors or processing circuitry of an apparatus causes the apparatus to implement an aspect of the method for estimating battery degradation in a heavy-duty vehicle or an embodiment thereof disclosed herein, wherein the computer program carrier is one of an electronic signal, optical signal, radio signal or computer-readable storage medium. [00052] Another aspect of the disclosed technology relates to a heavy-duty vehicle comprising a battery configured to charge an electric propulsion system, and an electronic control system, wherein the electronic control system comprises a memory comprising computer code which, wherein, when the computer code is loaded from the memory and executed by the one or processors or processing circuitry, causes the heavy-duty vehicle to perform a method of estimating an impact of a selected route on a state of health, SoH, of a battery in a heavy-duty vehicle. [00053] Another aspect of the invention relates to a heavy-duty vehicle comprising a battery configured to charge an electric propulsion system and an electronic control system, wherein the electronic control system comprises a memory comprising computer code which, wherein, when the computer code is loaded from the memory and executed by the one or processors or processing circuitry, causes the heavy-duty vehicle to perform a method for selecting a route for a heavy-duty vehicle. [00054] Another aspect of the invention relates to a heavy-duty vehicle comprising a battery configured to charge an electric propulsion system, for example, such as an electric vehicle or hybrid electric vehicle, and an electronic control system, wherein the electronic control system comprises a memory comprising computer code which, wherein, when the computer code is loaded from the memory and executed by the one or processors or processing circuitry, causes the heavy-duty vehicle to perform a method of estimating an impact of a selected route on a state of health, SoH, of a battery in a heavy-duty vehicle. [00055] Advantageously, by performing the method on the vehicle, the vehicle is able to present in some embodiments an indication to a driver of the vehicle of the effect of a candidate route being driven, about to be driven or which has been driven on the SoH of the battery of the vehicle. The method may be performed on the vehicle instead or in addition to being performed at a remote server such as a back-office server for a fleet of vehicles, where the vehicle is a member of the fleet, in some embodiments, [00056] In some embodiments, the heavy-duty vehicle is caused to perform an aspect of the method for selecting a route for a heavy-duty vehicle or an embodiment thereof disclosed herein, wherein the vehicle is configured to cause an indication of estimated battery degradation time obtained from performing the method for selecting a route for a heavy-duty vehicle for the selected candidate route when presenting the selected candidate route on the display. [00057] In some embodiments, the vehicle is configured to cause an indication of estimated battery degradation time for each candidate route when presenting a candidate route on the display. [00058] In some embodiments, the vehicle further comprises an advanced driving system configured to allow the vehicle to be driven autonomously, semi-autonomously, and/or to be remotely driven. [00059] The disclosed aspects and embodiments may be combined with each other in any suitable manner which would be apparent to someone of ordinary skill in the art. BRIEF DESCRIPTION OF THE DRAWINGS [00060] Some embodiments of the disclosed technology are described below with reference to the accompanying drawings which are by way of example only and in which: [00061] Figure 1A schematically illustrates an embodiment of a vehicle for which a method of battery heath state estimation according to the disclosed technology may be used to predict the battery health of the vehicle; [00062] Figure 1B schematically illustrates a method of battery state of health estimation according to some embodiments of the disclosed technology; [00063] Figure 1C schematically illustrates a method of battery state of health estimation according to some embodiments of the disclosed technology where traffic is modelled; [00064] Figures 2 illustrates schematically method for estimating an impact of a selected route on a state of health, SoH, of a battery of vehicle according to some embodiments of the disclosed technology; [00065] Figures 3A and 3B illustrate schematically typical force diagrams for vehicles; [00066] Figure 4 is a graph illustrating a speed profile comparison for two vehicles as they travel along a street in an example scenario; [00067] Figure 5A illustrates schematically a dynamic battery model according to some embodiments of the disclosed technology; [00068] Figure 5B illustrates schematically an example of a possible decomposition of a battery in terms of its SoC trajectories over N charging cycles; [00069] Figures 6A and 6B illustrates schematically a comparison between two simulations on the SoC of a vehicle battery according to some embodiments of the disclosed technology; [00070] Figure 7 illustrates schematically a long term comparison between two vehicles in terms of SoH; [00071] Figure 8 illustrates schematically a long term comparison between two vehicles in terms of energy costs; [00072] Figure 9A illustrates schematically a long term comparison between two vehicles in terms of delivery costs; [00073] Figure 9B illustrates schematically a long term comparison between two vehicles in terms of delay costs; [00074] Figure 10 illustrates schematically an embodiment of an apparatus configured to implement a method according to some embodiments of the disclosed technology; [00075] Figure 11A illustrates schematically an embodiment of another method according to the disclosed technology; [00076] Figure 11B illustrates schematically computer code for implementing the method of Figure 11A; and [00077] Figure 12 illustrates schematically an embodiment of another method according to the disclosed technology. DETAILED DESCRIPTION [00078] Aspects of the present disclosure will be described more fully hereinafter with reference to the accompanying drawings. The apparatus and method disclosed herein can, however, be realized in many different forms and should not be construed as being limited to the aspects set forth herein. Steps, whether explicitly referred to a such or if implicit, may be re-ordered or omitted if not essential to some of the disclosed embodiments. Like numbers in the drawings refer to like elements throughout. [00079] The terminology used herein is for the purpose of describing particular aspects of the disclosure only, and is not intended to limit the disclosed technology embodiments described herein. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. [00080] Figure 1A shows an embodiment of a vehicle 100, for example, a heavy-duty vehicle such as a truck, site machinery, digger, fork-lift truck, and the like. The vehicle 100 includes a battery power source which may be used to power internal system components including a propulsion system of the vehicle. The state of heath, SoH, of the battery or batteries of the vehicle may be modelled using a model 102 such as that shown schematically in Figure 1B. [00081] In some embodiments, the heavy-duty vehicle 100 is an electric vehicle, which has a battery configured to charge an electric propulsion system and an electronic control system, wherein the electronic control system comprises memory comprising computer code, and one or more processors or processing circuitry, wherein the computer code of the computer program, when loaded from the memory and executed by the one or processors or processing circuitry, is configured to cause the heavy-duty vehicle to perform, for example, a method 200 for estimating an impact of a selected route on a state of health, SoH, of a battery in a heavy-duty vehicle 100, such as a truck or semi-trailer according to the disclosed aspects and embodiments, for example, such the example embodiment shown in Figure 2 described herein below. [00082] In some embodiments, instead or in addition, the computer code comprises code configured to perform a method of selecting a route for the heavy-duty vehicle, for example, the computer code may comprise the code 1003 shown in Figure 10 and described herein below. [00083] In some embodiments, the computer code may comprises code configured to perform the method of selecting a route as shown in the example embodiments of Figures 11 or 12 as shown herein below for example. [00084] In some embodiments, heavy-duty vehicle is caused to perform the method of estimating battery degradation in a heavy-duty vehicle 100 such as a truck or semi-trailer, based on candidate routes and driving parameters. The heavy-duty vehicle 100 may also be configured to cause an indication of estimated battery degradation for the selected candidate route when presenting the selected candidate route on the display. The vehicle 100 may also be configured to generate an alert if a candidate route will cause the battery to degrade to a state which passes a threshold or other condition for alert generation. [00085] The heavy-duty vehicle may be any suitable form of electric vehicle, including, for example, a hybrid electric vehicle. The vehicle may be manually driven or not, for example, in some embodiments, the vehicle may further comprise an advanced driving system configured to allow the vehicle to be driven autonomously, semi-autonomously, and/or to be remotely driven, for example, from a remote server. [00086] The model 102 is for correlating vehicle usage and routing with battery degradation according to the disclosed embodiments. The relationship the model 102 establishes may be used to optimize vehicle routes, “r”, and vehicle parameters such as maximum allowed speed, v _max, and acceleration, a _max, in order to maximize the battery’s useful life while respecting deadlines and other operational constraints. [00087] The model 102 uses a vehicle 100 which has a set of points in space to visit (also referred to herein as missions), with known addresses. The model 102 allows the use of a degradation estimation to quantify a severity of any route, and uses this information to optimize mission planning, informing the best route, in terms of degradation, delay and energy consumption, as well as what should be the maximum speed and acceleration. [00088] The degradation can be modelled during charging of the battery and also, or instead, during discharging of the battery. The degradation of the battery which occurs as a result of both charging and discharging advantageously may provide a more accurate model of the battery. [00089] In some embodiments of the model 102, for example, that shown in Figure 1C, also includes a traffic modelling component 118. The traffic modelling component 118 models how the vehicle interacts with other vehicles along a particular route. This also allows for modelling of the vehicle’s speed changing along the route due to such interactions with other vehicles. The model 118 may also model the vehicle braking due to such interactions and/or to stop at traffic lights etc.. By modelling how the vehicle adjusts its speed through braking, in some embodiments, the battery degradation model models degradation of the battery during regenerative charging, which may occur, for example, as the battery undergoes braking. [00090] The model 102 may be implemented as a method, for example, as a computer-implemented method such as in the example embodiment of the method shown in Figure 2. [00091] According to the model 102, a decision epoch τ arrives whenever a set of missions is to be performed. The vehicles 102 are modelled starting from a known location (for example, a headquarters) and models the vehicles going back to the start at the end of the mission plan. [00092] The model 102 as shown in Figure 1B uses the following main hypotheses: all the information related to topology and nominal driving conditions is known in advance, where examples of such information include maximal allowed speed, road inclination, presence of crossroads, location of traffic lights, etc. (for example, see 104 in Figure 1B); the operational constraints related to deliveries by a vehicle are also known, including the list of all the points in space where deliveries must be made and their deadlines, in other words the vehicle’s route is known in advance (see 104 in Figure 1B); battery degradation and dynamics follow the models disclosed herein below, with all relevant parameters known in advance; and all relevant battery, for example, maximum charge, minimum charge, etc., and vehicle parameters, e.g. maximum speed and acceleration are known in advance. [00093] Some embodiments of the disclosed technology model how the battery state of health, SoH, evolves from a route profile. For example, in order to develop a comprehensive link between routes, maximum speed, maximum acceleration and battery SoH evolution, several models are combined. Some embodiments of a method according to the disclosed technology comprise using available road topology information to predict a power profile (shown as electrical power profile 108 in Figure 1B) for a vehicle to complete a given route, using the predicted power profile as input to a battery dynamic model shown in Figure 1B as KiBam + Second Order ECM 110 to create a predicted SoC profile 112 for the route, and using the SoC profile 112 in a battery degradation model 114 to provide the battery’s SoH evolution, shown as SoH prediction 116 in Figure 1B. [00094] In some embodiments, the Kibam model + ECM is replaced by Coulomb counting model + ECM. [00095] A quasi-static vehicle model and road topology according to some embodiments of the disclosed technology will now be described. Figure 3A of the drawings shows a generic vehicle, which may comprise a heavy duty vehicle such as is shown in Figure 3B of the drawings. [00096] Figures 3A and 3B both show schematically the usual forces applied on vehicle 100. By applying Newton’s second law and multiplying the resulting equation by the instantaneous speed v, one can [00097] obtain the instantaneous required mechanical power for a given speed v and acceleration a. where m is the total mass of the vehicle, g is the gravity acceleration, α is the instantaneous street inclination, Cr is the rolling resistance coefficient, Cw is the drag coefficient, A is the frontal area of the vehicle, and ρ is the air density. [00098] To convert P _mec to electrical power, it is necessary to account for the power train efficiency η(v, a) considered to be a function of instantaneous speed and acceleration. [00099] This function was obtained through a high fidelity truck simulator developed at the Volvo group, where different simulations had been performed and the ratio between electrical and mechanical power was analysed for different speeds and accelerations. Pelec = η(v, α)P _mec (2) [000100] In routing problems for EV’s, it is natural to translate information on the route (topology, traffic lights and so on), into expected speed and acceleration profiles. In Basso et al. (2019), for example, the authors considered that drivers would accelerate with constant acceleration until reaching road nominal speed and also accounted for traffic lights and crossroads, considering them as stop points where instantaneous speed must be zero. To achieve good results, they considered several particular cases, such as, for example, short street stretches, where nominal speed cannot be reached. [000101] Nowadays, it is possible to modify vehicle maximum speed and maximum acceleration remotely and, because those parameters can affect the P _elec 108 they are considered as optimization variables and be incorporated in the optimization problem described later herein below. [000102] Expected speed and acceleration profiles are built considering that vehicles will accelerate with their maximum acceleration until reaching either their maximum speed or road nominal speed. [000103] Figure 4 of the drawings shows a speed profile comparison for two vehicles 100a, 100b following the same route with different driving parameters. Vehicle 100a has the upper speed profile on the chart of Figure 4 and accelerates until road nominal speed with maximum possible acceleration while vehicle 100b has the lower of the two speed profiles shown on the chart of Figure 4. Vehicle 100b has its speed and acceleration limited. In the example speed profile comparison represented in Figure 4, the route followed by the vehicles 100a, 100b comprises a short street stretch with a stop point at the beginning and end. [000104] With these assumptions, the knowledge on the inclination of each route stretch and Equation (1), it is possible to predict a power profile 108 for each vehicle given a particular route and driving parameter. To connect routes to battery degradation, it is necessary to connect the power profile of the vehicle 108 to that vehicle’s battery SoC profile 112, which characterises a driving cycle. To do so, a battery dynamics model, 110, shown in Figure 1B as, for example, a dynamic battery model comprising a combined KiBam model and second order ECM model is used according to an embodiment of the disclosed technology. [000105] Figure 5A of the drawings shows in more detail an example of a Battery Dynamic Model 110 which is derived from Oliva et al. (2013) and which combines a Kinetic Battery Model (kiBam), for example, see Manwell and McGowan (1993), with a second order equivalent circuit model (ECM). The battery degradation model 110 can capture recovery and requires low computational effort, making it suitable for this application. The kiBam model an abstraction where the battery is seen as two wells, representing available charge and the bound charge. The kiBam models two parameters: capacity charge c and battery rate constant k which yield to two difference equations. ECM leads to two difference equations that can be used to infer battery voltage over time. The system of equations that describe the dynamic behaviour of the battery is:

[000106] where w1,k is the bound charge at instant k, W _2,k is the available charge, i _k is the current at instant k,v _s,k is the voltage difference on resistor s - with resistance R _s - and capacitor s - with capacitance C _s - at instant k, v _l,k is the voltage difference on resistor I - with resistance R _l and capacitor I with capacitance C _l . In this model, SoC at instant k can be directly obtained through:

[000107] where C _n is the battery nominal capacity. The input to the dynamic behaviour of the battery in equation (3) is the current, which allows the state of the SoC profile 112 shown in Figure IB to be estimated based on the electrical power profile 108 thanks to the relation:

[000108] Vbatt _k , the voltage of the battery at instant k is, in this model:

[000109] where Voc is the open circuit voltage defined by a SoC level and R _o is the resistance of resistor R _o shown in Figure 4 of the Battery Dynamic Model 110 which combined the kiBam model with a second order ECM model.

[000110] An embodiment of a battery degradation model 110, for example, the KiBam + Second order ECM, as shown in Figure 4 and in the embodiment of the battery state of health estimation model 102 in Figure IB will now be described.

[000111] Battery degradation is usually defined in terms of the capacity of the battery. It is a very standard approach to consider the state of health (SoH) of a battery as: [000112] where C _τ is the maximum capacity of the battery at the decision epoch τ for a mission in other words for a planned router that the vehicle will undertake, and C _n is its nominal capacity. When SoH falls under a given threshold - which changes according to battery application - the battery must be replaced.

[000113] Because degradation in batteries is a very complex phenomenon, different techniques have been employed to estimate end of life and model degradation. Considering that machine learning algorithms were implemented, as well as stochastic approaches and physics based models, one can conclude that scientific community has not yet converged to a model capable of capturing the full reality of the degradation process, nonetheless, battery stress factors are well-known, and most authors agree that depth of discharge(DoD), mSoC and temperature are among the main drivers of cycle degradation.

[000114] Without loss of generality, since the proposed approach for optimization of routes will affect the stress factors themselves and can be employed with different modelling approaches that can account for other stress factors related to SoC profile - the chosen model for degradation is an empirical one, based on the version presented by Xu et al. (2018), where those aforementioned stress factors are considered. Assuming that the SoC history can be expressed as a combination of N elementary SoC cycles, such as Figure 5B shows, the SoH is consider to vary according to:

SoH = e ^-fd (8A)

[000115] where f _d is a function of the stress factors chosen.- In other words, over N cycles, the SoH degrades according to:

[000116] Where f _d (N) is a degradation function evaluated on the N SoC cycles, accounting for the effect of mSoC, DoD, and temperature as the main battery stress factors. For each cycle i in the SoC history, mSoC is assesses as the mean value of the cycle, DoD as the amplitude δ _i of discharge of that i ^th cycle, and the temperature as the average temperature T _i for the cycle.

[000117] A battery degradation function according to the disclosed technology can then be evaluated based on battery cycling degradation which yields:

[000118] where N is the number of cycles, i is an index that indicates each cycle, wi is 1 for a full cycle or 0.5 for a partial cycle. S _δ , S _σ and S _τ are stress factors related to DoD, SoC and temperature respectively. Figure 5B shows an example of a possible decomposition of a SoC trajectory in N battery charging and discharging cycles. These stress factors are usually empirically determined, and the chosen functions, taken from Xu et al. (2018) are:

[000119] Or alternatively by:

The terms k _σ , k _τ ,k _δ1 ,k _δ2 and k _δ3 are constants empirically determined through experiments and σ _ref and T _ref are respectively the experiment reference values for mSoC and temperature respectively. Both σ, δ can be computed through the usage of the Rainflow-Counting algorithm Matsuichi and Endo (1968) on SoC profile. T can be computed as simply the average temperature of each cycle. Throughout this work temperature will be considered as a normally distributed random variable centred around the average temperature that should be guaranteed by the battery management system of the vehicles, for example, by the battery management system of heavy duty vehicles such as trucks.

[000120] With the degradation model established, using the predicted SoC profile 112, it is possible to estimate cycle degradation for a given route and driving parameters, according to the example models shown in Figure 1B or 1C.

[000121] Some embodiments of the disclosed technology optimize vehicle usage acting on the three decision variables: r that represents the chosen route to fulfil a mission, V _max that is the maximum allowed speed of a vehicle and a _max , the maximum allowed acceleration.

[000122] The disclosed technology seeks to find the best exploitation strategy for a vehicle, which is in some embodiments modelled as an optimization problem.

[000123] In some embodiments, instead of modelling a single vehicle, the disclosed technology can be used to model a group of vehicles, for example, a fleet of vehicles where a fleet of vehicles may also share a common back office server in some embodiments.

[000124] For example, in order to find the best exploitation strategy for a vehicle 100, minimizing degradation is not enough, since there are other costs related to missions, for example, other operational costs. The disclosed technology takes into account delay costs and energy costs which leads to a cost C that can be expressed as:

C = C _delay + C _energy + C _deg (11A)

In other words as:

C(r, _max , v _max ,a _max ) = C _delay (r, v _max , a _max ) + C _energy (r, v _max , a _max ) +

C _deg (r, v _max , a _max ) (11B)

Delay cost is considered to be proportional to delays themselves and can be expressed as:

[000125] In other words as: C _delay (r, v _max , a _max ) = C _d max [t(r, v _max , a _max ) — I, 0] (12B)

[000126] C _d is a constant that is related to the cost of penalties, P is the total number of points to be visited, t _i is the arrival time at point i and l _i is the deadline of point I, in other words I is the mission deadline for point i. Similarly, energy cost is considered directly proportional to the consumed energy:

[000127] where C _e is the price of the kW h, e _i is the energy spent by a vehicle i and M represents the full fleet of vehicles.

[000128] In other words, the energy cost used in some embodiments of the method of battery state of health estimation, or in a method of battery degradation as: C _energy (r, v _max , a _max ) C _e e (r, v _max , a _max ) (13B) where Ce is the price of the kW h, e(r, V _max , a _max ) is the expected energy spent in the mission given r,v _max and a _max , obtained by integrating the expected P _elec .

Finally, to account for battery degradation, we consider C, that can be written as:

[000130] In other words, in some embodiments, the degradation cost is modelled as C _deg (r, V _max , a _max ) = C _bat ΔSoH( r, v _max , a _max ) (14B) where C _bat is the price of a new battery and ASoH is the expected variation of SoH(r, v _max , a _max ) after completing a mission with a route r, maximum speed v _max and maximum acceleration a _max .

[000131] The expected variation of SoH can then computed based on the method proposed in Fig 2 using the model of Figure 1B, and a complete cycle degradation estimation algorithm described herein which uses the model of Figure 1B whose functional components are described herein above. Some embodiments of the complete cycle degradation estimation algorithm use aforementioned models, for given route and driving parameters to estimate an expected power profile for a vehicle's route, which can be used in turn to obtain an expected SoC profile for the vehicle's battery that is used to infer how a battery will with each charging cycle degrade, in other words, how the battery's state of health SoH, decreases over time caused by the vehicle's displacement along a route, for example, see Fig 5B.

[000132] In some embodiments of the disclosed technology, method 200, for example the method shown in Figure 11B, is used to optimize routing and driving parameters for a vehicle 100, for example, a heavy-duty vehicle such as a truck or the like. The driving parameters which are used by an optimization framework according to some embodiments of the disclosed technology include maximum speed and acceleration parameters.

OPTIMIZATION FRAMEWORK

[000133] The optimization problem comprises terms which are computed using the above mentioned models and hypotheses in some embodiments which enable the optimization problem to be expressed as finding a route r, maximum speed v _max and acceleration a _max that minimizes the cost function C, for example, as set out below in equations (15A) and (15B). For example, in some embodiments, the optimization problem can be expressed as follows:

[000134] and this may be solved, in some embodiments, using a suitable algorithm, for example, an artificial intelligence, neural networking algorithm or a genetic programming model. An example of a genetic algorithm, adapted from http://www.cs.ucc.ie/~dgb/courses/tai/notes/handout12.pfdf , is provided below which may be used to solve an example embodiment of the battery optimization problem in pseudo code. The genetic algorithm can be expressed as:

Algorithm: GA(n, χ, μ)

// Initialise generation 0: k := 0;

P _k := a population of n randomly-generated individuals;

// Evaluate Pk:

Compute fitness(i) for each i ∈ P _k ; do { // Create generation k + 1:

// 1. Copy:

Select (1 - χ) × n members of P _k and insert into P _k+1 ;

// 2. Crossover:

Select χ × n members of P _k ; pair them up; produce offspring; insert the offspring into

Pk+1;

// 3. Mutate:

Select μ x n members of P _k+1 ; invert a randomly-selected bit in each;

// Evaluate Pk+1:

Compute fitness(i) for each i ∈ P _k ;

// Increment: k := k + 1;

} while fitness of fittest individual in Pk is not high enough; return the fittest individual from P _k ; In the above pseudo code, n is the number of individuals in the population, in other words, the number of routes, χ is the fraction of the population to be replaced by crossover in each iteration, and μ is the mutation rate. Another example of a genetic algorithm suitable for solving the optimization problem is disclosed in "A Genetic Algorithm for Shortest Path Routing Problem and the Sizing of Populations" by Chang Wook Ahn and R.S. Ramakrishna in IEEE Transactions on Evolutionary Computation, Vol. 6, No. 6, December 2002, page 566.

[000135] In some embodiments of the optimization problem, whenever a new mission must be completed, a decision epoch τ occurs. Here a mission comprises a planned route that a vehicle is to follow with certain constraints, such as time of arrival, maximum speed etc. The optimization problem according to some of the disclosed embodiments which is to be solved can also be expressed in the following form: where r, v _max , and a _max refer to the route, the maximum speed along the route or velocity of the vehicle, and the maximum acceleration of the vehicle, and C is the exploitation cost for the mission in that decision epoch τ.

[000136] The optimization algorithm in this example uses a vehicle's planned route (or mission) topology information, the vehicle's battery initial SoC, all the relevant battery parameters and an embodiment of a battery dynamic model as set out hereinabove, to compute C(r, vmax, amax) for a given route, and hence find the best exploitation cost for the mission decision epoch τ. In some embodiments, the optimization algorithm may comprise computer code which when executed performs an embodiment of the method 200, and it may also be used by the method 1100 of Figure 11, described later below in some embodiments.

[000137] This optimization problem may be solved using any suitable machine learning or neural network based algorithm, in other words, any suitable genetic programming algorithm may be used such as, for example, those mentioned above.

[000138] In some embodiments, to estimate the performance of the optimization method and the degradation prediction based on routes, traffic simulation was included in the model 102. In some embodiments, SUMO (Lopez et al. (2018)) was used. SUMO is an open source, microscopic, multi-modal traffic simulator. By including a traffic simulator like SUMO, the model 102 can quantify how the randomness of a more realistic environment can affect degradation estimation based on routes as well as the impact of route optimization in the long term.

[000139] Following the model of Fig. 1 and the method of Figure 2, for a given route, a maximum vehicle speed and a maximum vehicle acceleration, it is possible to estimate the degradation caused by a displacement. However, this prediction is subjected to uncertainty that arises from traffic conditions where vehicles interact with each other, which causes unpredicted stops, deceleration and even acceleration, impacting the quality of the SoC profile estimation when compared to the actual one.

[000140] To estimate performance of the optimization method and the degradation prediction based on routes where other vehicles are travelling, in other words where there is traffic, a traffic-simulator may be included in the model 102. For example, in some embodiments, SUMO (Lopez et al. (2018)), an open source, microscopic, multi-modal traffic simulator, can be used to reproduce different traffic scenarios. Embodiments of the model 102 which include a traffic simulator such as SUMO, however, make it possible to know how the randomness of a more realistic environment can affect degradation estimation based on routes as well as the impact of route optimization in the long term.

[000141] Figure 1C of the drawings shows an example of the model 102 where a traffic simulator model 118 such as SUMO has been included. By executing computer code representing the model 102 shown schematically in Figure 1B, a method such as that shown in Figure 2 may be executed which allows, given a route, a maximum vehicle speed and a maximum vehicle acceleration in 104, an idealised or free-flow estimate of an electric vehicle's battery degradation to be assessed based on that vehicle's displacement.

[000142] Such a prediction however is subjected to incertitude that arises from traffic conditions. Vehicles 100 interact with each other, which causes unpredicted stops and deceleration, impacting the quality of the SoC profile estimation.

[000143] Figures 6A and 6B show a comparison between speed and SoC profile, both in a simulation 602a with no other vehicle traffic, in other words a free flow, and in a simulation 604a with other vehicles, in other words in traffic, randomly moving through space.

[000144] In the free flow simulation 602a represented in Figure 6A, the vehicle 100 can freely accelerate until reaching road nominal speed, at which it remains having to break only once due to a curve. The simulation 604a with more vehicles starts similarly but while in road nominal speed, the vehicle 100 reaches a point of the route where it interacts with other vehicles, having to brake and keeping a speed inferior to the nominal one, until it reaches a point where it can accelerate once again.

[000145] The presence of other vehicles affected SoC trajectory 604b as shown in the example comparison of Figure 6B. In the free flow simulation 602b, due to the bigger average speed, charge was consumed faster in steady speed than for the simulation 604b which modelled the vehicle interacting with traffic type conditions along the route. In this example embodiment, however, because charge is intensively consumed while accelerating, which happened more often in the scenario 604b which included more vehicles, at the end of both simulations 602b, 604b, the battery SoC level remained similar. It is expected that similar low variance in battery degradation and energy consumption may occur in similar simulations.

[000146] To quantify how traffic randomness affects cycle degradation estimation, Monte Carlo simulations were carried out. In all simulations a random number of vehicles make random displacements and a chosen vehicle performs the same route with imposed maximum speed and acceleration. This information is used to estimate the battery degradation function for N SoC cycles, f _d (N), based on the SoC trajectory in each of the random displacements, in the model presented in Figure IB, in other words, when performing the method of battery SoH estimation of Figure 2.

[000147] The error for free flow scenarios, in other words, the normalized error between expected f _d and simulated f _d can be seen in Table 1 below:

Table 1 showing the effect of random traffic on f _d (N) estimation.

[000148] As can be seen, the error for free flow scenarios is around 6%, which reflects the difference between speed and acceleration profiles predicted using the model of Figure IB and the models which used SUMO simulations. The error value remains constant for scenarios with few vehicles, however, with more than 100 random vehicles in the simulation, the vehicle interactions start reducing the accuracy of the f _d estimation.

LONG-TERM ROUTE IMPACT ON BATTERY HEALTH

[000149] Since SoH evolves slowly, the effect of an individual cycle is negligible, however, the choice of route and driving parameters can have an impact in the long term. [000150] Some embodiments of the disclosed technology use a long-term simulation to compare two vehicles that will perform the same mission in every working session with different routes and driving parameters.

[000151] In some embodiments, the long term simulation set-up is as follows:

• All simulations were performed in the same n x n street-grid, for example, a 7x7 street grid, such as a 7 x 7 Manhattan street grid which was used in one example simulation, which contained streets with different nominal speeds.

• In each simulation, where a simulation is also referred to herein as a working session, the vehicles all start at the same location and make a delivery at the same point in space.

• Vehicle 1, also shown in Figures 7 and 8 as vehicle 100a , will follow the route found whilst minimizing the overall expected cost C(r, vmax, amax), see equation (11), with the respective driving parameters, while Vehicle 2, also shown in Figures 7 and 8 as vehicle 100b will follow the fastest route, with no limitations in terms of acceleration and speed, emulating a real driver.

• At the each simulation, SoH, delay cost is determined, for example, using equation 12A (or 12B) and energy cost is determined, for example, using equation 13A (or (3B).

• Each simulation will happen with random traffic conditions (a random number of vehicles will perform random displacements).

[000152] The constant values of the cost constraints of the optimization problem were all the same value for C _bat , C _d , and C _e , and in one example embodiment the values selected were C _bat = 5000, C _d = 10($/min) and C _e = 0.1($/kW h).

[000153] Figure 7 shows the results of some example simulations for each of the vehicles 100a, 100b to provide a comparison of SoH evolution. Vehicle 1, 100a, follows the optimal route according to equation (15A or 15B) which can be seen that it has impacted SoH evolution positively. Because simulations were limited to 200 working sessions, both vehicles remained far from end of life. On the other hand, since SoH evolves slowly, one can conclude that a small improvement on each driving cycle can have a huge impact on the number of working sessions until failure. In this example linearly extrapolating SoH trajectory for both vehicles, for an end of life threshold of 80%, vehicle 1, 100a would have approximately 300 extra working sessions until battery replacement.

[000154] Figure 8 shows the comparison between energy costs. Because vehicle 2, 100b had limitations on maximum acceleration and speed, it consumed less energy, impacting its energy consumption cost. Figure 8 also shows delays costs in the case where vehicle 2, 100b has outperformed vehicle 1, 100a, due to limitations on speed and acceleration. The optimal schedule found presented a null expected delay but, due that traffic randomness, in some work sessions penalties were paid. A real time probabilistic optimization algorithm that takes into account current traffic conditions could improve this aspect. Overall, the reduction in terms of energy consumption compensates the delay costs and the optimization algorithm has reduced the total exploitation cost and postponed battery replacement, which can have a huge impact on real life applications, especially if applied to a fleet of vehicles with several deliveries to be performed every day.

[000155] The disclosed technology provides a method for estimating cycle degradation on a battery for a given route, maximum vehicle speed and acceleration. This method may be used to solve a routing problem considering battery degradation, delays and energy consumption.

[000156] The performance of optimization was validated through simulations with random traffic conditions. In terms of the impact of routes on battery degradation, it was shown that, optimizing routes on the exploitation cost and useful life duration of the battery.

[000157] From the modelling point of view, in future works, battery dynamics and degradation will be represented by more realistic and robust models, and the prediction of degradation based on a given route will be validated with real vehicle data. The optimization problem can involve more realistic constraints, such as charging necessity, delivery time, vehicle storage capacity, and more importantly, this optimization problem must be extended to the fleet, so that decisions on which vehicle to use depending on its SoH can be made. It is also important to highlight that traffic conditions can impact delays and therefore, it is important to incorporate real time traffic information in future works, providing real time routing. Other actions than routing and limiting speed or acceleration can be applied. For instance, it would be interesting to consider optimal charging strategies in future decision making problems.

[000158] Another crucial decision to be made is when to replace batteries of a vehicle, which is affected by vehicle exploitation. Different maintenance strategies must be also considered in future works. When all those actions are considered together, decisions will happen in different time scales (maintenance and replacements happen rarely throughout the life of a vehicle, while routing and charging happen in a daily basis), therefore it is necessary to make them in a closed loop fashion, taking into account randomness and the effect of previous actions in the system.

[000159] In some embodiments, the electric vehicle may be a heavy-duty electric vehicle 100. A heavy-duty electric vehicle 100 may comprise a wide range of different physical devices, such as electric propulsion systems, and for hybrid vehicles also combustion engines, electric machines, friction brakes, regenerative brakes, shock absorbers, air bellows, and power steering pumps. These physical devices are commonly known as Motion Support Devices (MSD). The MSDs may be individually controllable, for instance such that friction brakes may be applied at one wheel, i.e., a negative torque, while another wheel on the vehicle, perhaps even on the same wheel axle, is simultaneously used to generate a positive torque by means of an electric machine.

[000160] In some examples of the disclosed embodiments, the vehicle 100 is an autonomous vehicle with an ADS configured to make tactical decisions for a control system. The autonomous operation of a heavy-duty vehicle is accordingly more complex than the autonomous operation of a more light-weight vehicle such as a car.

[000161] Some, if not all, of the above embodiments may be implemented using computer program code which may be provided as software or hardcoded, for example, as a computer program product configured to be used by a device mounted on or integrated in a vehicle 100. In some embodiments, the computer program product comprises computercode which when executed by one or more processors of the vehicle 100, causes the vehicle to implement a method 100 according to any one of the disclosed embodiments. [000162] However, in some embodiments , the methods disclosed herein are performed off-board, for example, at a back-office server for a fleet of vehicles, including the heavy-duty vehicle which has the battery whose degradation is being modelled according to the disclosed technology.

[000163] Figure 10 of the accompanying drawings shows an example apparatus 1000 comprising memory 1001, one or more processors or processing circuitry 1002. A computer program comprising computer code 1003 is stored in memory 1001 and when the computer code 1003 is loaded from memory 1001 and executed by the one or more processors or processing circuitry 1002, the apparatus 1000 is caused to perform a method 200 as shown in Figure 2 of the drawings according to some embodiments of the disclosed technology.

[000164] In Figure 2, an embodiment of a method 200 to estimate an impact of a selected route on a state of health, SoH, of a battery in a heavy-duty vehicle 100, such as a truck or semi-trailer is shown schematically. In the embodiment of Figure 2, the method 200 comprises predicting a required power profile for a given route at least partly based on a road topology of the route 202, configuring a dynamic battery model 204, feeding the predicted power profile to the dynamic battery model 206, and thereby obtaining a predicted state of charge, SoC, profile for the given route 208, configuring a degradation model for the battery of the heavy-duty vehicle 210 and feeding the predicted SoC profile of the route to the degradation model 214, thereby obtaining the impact of the selected route on the SoH of the battery 216.

[000165] Returning now to Figure 10, the computer code 1003 comprises in some embodiments, one or more modules or circuitry 1004-1016, for example, as shown in Figure 10, where the computer program code is configured to perform method 200 to implement an embodiment of the model shown in Figure 1B of the drawings, the computer program code comprises a Route + Driving parameters module 1004, an off-line acceleration profile prediction + Newton's law module 1006, an electrical Power profile module 1008, a dynamic battery model module 1010, a SoC Profile module 1012, a battery degradation model module 1014, and a battery SoH prediction module 1016.

[000166] In some embodiments, the module 1008 predicts a required power profile for a vehicle to follow a given route at least partly based on a road topology of the route determined using module 1004 and module 1006.

[000167] In some embodiments, module 1010 is used to configure a dynamic battery model, and SoC profile module 1012 obtains a predicted SoC profile for the given route using module 1008 and battery module configured using module 1010.

[000168] In some embodiments, the battery degradation model module 1014, for example, is used to model the degradation of a battery of a vehicle such as a heavy-duty vehicle 100 as shown in Figure 1A, for example, a truck or the like.

[000169] In some embodiments, the predicted route which is output of the predicted SoH profile of module 1012 is fed into the battery degradation module 1014 to obtain the impact of the selected route on the SoH of the battery using the battery SoH prediction module 1016.

[000170] In some embodiments, the selected route comprises a set of points in space to visit, with known addresses. The selected route may be associated with information related to vehicle speed and/or vehicle acceleration.

[000171] In some embodiments, a required power profile is based on a required mechanical power of the selected route and on an efficiency of a power train of a heavy- duty vehicle 100.

[000172] In some embodiments, a required power profile is based on an efficiency of a power train of a heavy-duty vehicle 100.

[000173] In some embodiments, the dynamic battery model combines a Kinetic Battery Model, kiBam, with a second order equivalent circuit model, ECM.

[000174] In some embodiments, battery degradation is defined in terms of a capacity degradation of the battery.

[000175] Figure 11A shows schematically another embodiment of the disclosed technology comprising a method 1100 for selecting a route for a heavy-duty vehicle (100), comprises identifying a set of candidate routes in 1102, configuring a cost function comprising a state of health, SoH, evolution (C _deg ) of a battery on the heavy-duty vehicle 100 in 1104, evaluating each route in the set of routes according to the configured cost function in 1106, and selecting the route based on the evaluation in 1108.

[000176] In some embodiments, the apparatus 1000 instead or in addition comprises modules 1112 to 1118 configured to implement an embodiment of method 1100 instead of or in addition to modules 1004 to 1016 which are configured to implement an embodiment of method 200. For example, as shown in Figure 11B, the computer code 1003 comprises a candidate route identification module 1102, which when loaded from memory 1001 and executed by one or more processors or processing circuitry of the apparatus 1000 is configured to identify a set of candidate routes, a cost function configuration module 1114, which when loaded from memory 1001 and executed by the one or more processors or processing circuitry of apparatus 1000 is configured to configure a cost function comprising a state of health, SoH, evolution (C _deg ) of a battery on a vehicle such as the heavy-duty vehicle 100. In some embodiments, the cost function comprises an energy consumption cost (C _energy ) and/or a cost associated with route delay (C _delay ). The computer code 1003 also comprises a route evaluation module 1116 configured when executed to evaluate each route in the set of routes according to the configured cost function generated by the cost function configuration module 1114, and a route selection module 1118 which is configured, when executed, to cause selection of a route based on the evaluation performed by the route evaluation module 1116.

[000177] In some embodiments, the apparatus 1000 instead or in addition comprises one or more modules configured to perform a method 1200 for estimating battery degradation in a heavy-duty vehicle 100 such as a truck or semi-trailer, based on route candidates and driving parameters, wherein the method comprises integrating a decision making optimization problem that finds the best route, maximum speed and acceleration in terms of energy consumption, degradation and delay.

[000178] Figure 12 shows an example of the method 1200 which comprises obtaining one or more route candidates and driving parameters in 1202, generating an optimization problem for the decision making optimization problem in 1204, and finding as a solution to the optimization problem in 1206, one or more or all of: a best route for the heavy-duty vehicle 100 to follow, a maximum speed of the heavy-duty vehicle, and a maximum acceleration of the vehicle.

[000179] In some embodiments, the optimization problem comprise finding a solution to a cost function for a state of health evolution of a battery of the heavy-duty vehicle 100 based on a power profile for the vehicle indicating an energy consumption of the vehicle along a route, a battery degradation model for the battery of the vehicle, and a route delay cost function. The route delay cost function may also include a cost function generated by predicted traffic delays along a route using a suitable traffic simulator model, for example, a SOHO simulator model.

[000180] In some embodiments, the modules are configured at least party in circuitry, in other words, they may be hard-coded.

[000181] For example, the methods described above may be at least partly implemented through one or more processors or processing circuitry in a control unit of a vehicle 100 together with computer program code for performing the functions and actions of the embodiments described herein. In other words, in some embodiments, the apparatus 1000 may comprise a vehicle 100.

[000182] Alternatively, the methods and models disclosed herein may be performed by apparatus 1000 comprising a remote server, for example, they may be performed by a back-office server for a fleet of vehicles 100 for each vehicle's battery.

[000183] In some embodiments, the program code mentioned above may also be provided as a computer program product, for instance in the form of a data carrier carrying computer program code or code means for performing the embodiments herein when being loaded into the processing circuitry of a controller or control unit of vehicle 100. The data carrier, or computer readable medium, may be one of an electronic signal, optical signal, radio signal or computer-readable storage medium. The computer program code may e.g. be provided as pure program code in the controller or on a server and downloaded to the controller. Thus, it should be noted that the functions of the controller may in some embodiments be implemented as computer programs stored in memory, for example, a computer readable storage unit, for execution by processors or processing modules, e.g. the processing circuitry in the control unit or controller.

[000184] Those skilled in the art will also appreciate that the processing circuitry and the memory or computer readable storage unit described above may refer to a combination of analog and digital circuits, and/or one or more processors configured with software and/or firmware, e.g. stored in a memory, that when executed by the one or more processors such as the processing circuitry perform as described above. One or more of these processors, as well as the other digital hardware, may be included in a single application-specific integrated circuit (ASIC), or several processors and various digital hardware may be distributed among several separate components, whether individually packaged or assembled into a system-on-a-chip (SoC).

[000185] The control unit may also comprise or is capable of controlling how signals are sent wirelessly via antenna from a vehicle such as a heavy duty vehicle in order for the vehicle to communicate via one or more communications channels with remote entities, for example, a site back office in some embodiments.

[000186] In some embodiments, the vehicle 100 is a heavy-duty vehicle which is autonomous, or semi-autonomous or remote controlled, in which case the back-office server may be configured to monitor the vehicle and/or to remotely control the vehicle 100. [000187] The communication channels the vehicle 100 and/or back office uses to communicate may be point-to-point, or networks, for example, over cellular or satellite networks which support wireless communications. The wireless communications may conform to one or more public or proprietary communications standards, protocols and/or technologies, including but not limited to Global System for Mobile Communications (GSM), Enhanced Data GSM Environment (EDGE), high-speed downlink packet access (HSDPA), wideband code division multiple access (W-CDMA), code division multiple access (CDMA), time division multiple access (TDMA), Bluetooth, Wireless Fidelity (Wi-Fi) (e.g., IEEE 802.11a, IEEE 802.11b, IEEE 802.11g and/or IEEE 802. lln), voice over Internet Protocol (VoIP), WiMAX, a protocol for email (e.g., Internet message access protocol (IMAP) and/or post office protocol (POP)), instant messaging (e.g., extensible messaging and presence protocol (XMPP), Session Initiation Protocol for Instant Messaging and Presence Leveraging Extensions (SIMPLE), and/or Instant Messaging and Presence Service (IMPS)), and/or Short Message Service (SMS)), or any other suitable communication protocol, including communication protocols not yet developed as of the filing date of this document.

[000188] The operating system of the vehicle may further various software components and/or drivers for controlling and managing general system tasks (e.g., memory management, storage device control, power management, etc.) and facilitates communication between various hardware and software components.

[000189] Where the disclosed technology is described with reference to drawings in the form of block diagrams and/or flowcharts, it is understood that several entities in the drawings, e.g., blocks of the block diagrams, and also combinations of entities in the drawings, can be implemented by computer program instructions, which instructions can be stored in a computer-readable memory, and also loaded onto a computer or other programmable data processing apparatus. Such computer program instructions can be provided to a processor of a general purpose computer, a special purpose computer and/or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer and/or other programmable data processing apparatus, create means for implementing the functions/acts specified in the block diagrams and/or flowchart block or blocks.

[000190] In some implementations and according to some aspects of the disclosure, the functions or steps noted in the blocks can occur out of the order noted in the operational illustrations. For example, two blocks shown in succession can in fact be executed substantially concurrently or the blocks can sometimes be executed in the reverse order, depending upon the functionality/acts involved. Also, the functions or steps noted in the blocks can according to some aspects of the disclosure be executed continuously in a loop.

[000191] The description of the example embodiments provided herein have been presented for the purposes of illustration. The description is not intended to be exhaustive or to limit example embodiments to the precise form disclosed, and modifications and variations are possible in light of the above teachings or may be acquired from practice of various alternatives to the provided embodiments. The examples discussed herein were chosen and described in order to explain the principles and the nature of various example embodiments and its practical application to enable one skilled in the art to utilize the example embodiments in various manners and with various modifications as are suited to the particular use contemplated. The features of the embodiments described herein may be combined in all possible combinations of methods, apparatus, modules, systems, and computer program products. It should be appreciated that the example embodiments presented herein may be practiced in any combination with each other.

[000192] It should be noted that the word "comprising" does not necessarily exclude the presence of other elements, features, functions, or steps than those listed and the words "a" or "an" preceding an element do not exclude the presence of a plurality of such elements, features, functions, or steps. It should further be noted that any reference signs do not limit the scope of the claims, that the example embodiments may be implemented at least in part by means of both hardware and software, and that several "means", "units" or "devices" may be represented by the same item of hardware.

[000193] The various example embodiments described herein are described in the general context of methods, and may refer to elements, functions, steps or processes, one or more or all of which may be implemented in one aspect by a computer program product, embodied in a computer-readable medium, including computer-executable instructions, such as program code, executed by computers in networked environments.

[000194] A computer-readable medium may include removable and non-removable storage devices including, but not limited to, Read Only Memory (ROM), Random Access Memory, RAM), which may be static RAM, SRAM, or dynamic RAM, DRAM. ROM may be programmable ROM, PROM, or EPROM, erasable programmable ROM, or electrically erasable programmable ROM, EEPROM. Suitable storage components for memory may be integrated as chips into a printed circuit board or other substrate connected with one or more processors or processing modules, or provided as removable components, for example, by flash memory (also known as USB sticks), compact discs (CDs), digital versatile discs (DVD), and any other suitable forms of memory. Unless not suitable for the application at hand, memory may also be distributed over a various forms of memory and storage components, and may be provided remotely on a server or servers, such as may be provided by a cloud-based storage solution. Generally, program modules may include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types.

[000195] Computer-executable instructions, associated data structures, and program modules represent examples of program code for executing steps of the methods disclosed herein. The particular sequence of such executable instructions or associated data structures represents examples of corresponding acts for implementing the functions described in such steps or processes.

[000196] The memory used by any apparatus whatever its form of electronic apparatus described herein accordingly comprise any suitable device readable and/or writeable medium, examples of which include, but are not limited to: any form of volatile or non-volatile computer readable memory including, without limitation, persistent storage, solid-state memory, remotely mounted memory, magnetic media, optical media, random access memory (RAM), read-only memory (ROM), mass storage media (for example, a hard disk), removable storage media (for example, a flash drive, a Compact Disk (CD) or a Digital Video Disk (DVD)), and/or any other volatile or non-volatile, non-transitory device readable and/or computer-executable memory devices that store information, data, and/or instructions that may be used by processing circuitry.

[000197] Memory may store any suitable instructions, data or information, including a computer program, software, an application including one or more of logic, rules, code, tables, etc. and/or other instructions capable of being executed by processing circuitry and, utilized by the apparatus in whatever form of electronic apparatus. Memory may be used to store any calculations made by processing circuitry and/or any data received via a user or communications or other type of data interface. In some embodiments, processing circuitry and memory are integrated. Memory may be also dispersed amongst one or more system or apparatus components. For example, memory may comprises a plurality of different memory modules, including modules located on other network nodes in some embodiments.

[000198] In the drawings and specification, there have been disclosed exemplary aspects of the disclosure. However, many variations and modifications can be made to these aspects which fall within the scope of the accompanying claims. Thus, the disclosure should be regarded as illustrative rather than restrictive in terms of supporting the claim scope which is not to be limited to the particular examples of the aspects and embodiments described above. The invention which is exemplified herein by the various aspects and embodiments described above has a scope which is defined by the following claims.

LIST OF REFERENCES

Basso, R., Kulcs'ar, B., Egardt, B., Lindroth, P., and Sanchez-Diaz, I. (2019). Energy consumption estimation integrated into the electric vehicle routing problem. Transportation Research Part D: Transport and Environment, 69, 141-167.

Jbili, S., Chelbi, A., Radhoui, M., and Kessentini, M. (2018). Integrated strategy of vehicle routing and maintenance. 170, 202-214. doi:10.1016/j.ress.2017.09.030.

Lopez, P.A., Behrisch, M., Bieker-Walz, L., Erdmann, J., Fl' otter 'od, Y.P., Hilbrich, R., L ^{. .} ucken, L., Rummel, J., Wagner, P., and Wieβner, E. (2018). Microscopic traffic simulation using sumo. IEEE Intelligent Transportation Systems Conference (ITSC).

Manwell, J.F. and McGowan, J.G. (1993). Lead acid battery storage model for hybrid energy systems. 50(5), 399-405. doi:https://doi.org/10.1016/0038- 092X(93)90060-2.

Matsuichi, M. and Endo, T. (1968). Fatigue of metals subjected to varying stress. Oliva, J. A., Weihrauch, C., and Bertram, T. (2013). Model-based remaining driving range prediction in electric vehicles by using particle filtering and markov chains. In 2013 World Electric Vehicle Symposium and Exhibition (EVS27), 1-10. doi: 10.1109/EVS.2013.6914989.

Robert, E., Bouvard, K., Lesobre, R., and B'erenguer, C. (2019). Joint assignment of missions and maintenance operations for a fleet of deteriorating vehicles. In Proc, of 11th International Conference on Mathematical Methods in Reliability - MMR2019, City University Hong-Kong, Jun 2019, Hong-Kong, China.

Xu, B., Oudalov, A., Ulbig, A., Andersson, G., and Kirschen, D.S. (2018). Modeling of lithium- ion battery degradation for cell life assessment. IEEE Transactions on Smart Grid, 9(2), 1131-1140. doi: 10.1109/TSG.2016.2578950.