1 Introduction

Since several years the automotive industry has been experiencing the introduction and utilization of Intelligent Transport Systems (ITSs) to attribute vehicles and the surrounding infrastructure with intelligent features [1, 2]. Following the above trend, the introduction of Highly Automated Vehicles (HAVs) with a variety of sensing capabilities (computer vision, radars, LiDAR, ultrasonics), being able to analyze and handle vast amounts of data from sensors associated with the “understanding” of the complex driving environment scene, is a crucial factor for HAVs towards achieving the desired levels of autonomy and ensuring safety for the driver and the passengers [3]. In this respect, efficient on-board ITSs are of fundamental importance to enhance travel experience with HAVs.

In recent years, cognitive features have been added to ITSs, mainly by utilizing empirical data as the basis for learning the input features-parameters through causal reasoning Artificial Intelligence (AI) data-driven techniques (e.g., machine learning, deep learning, etc.) [4]. Such a technique provides ITSs with important features being able to make real-time decisions and solve complicated problems. Therefore, intelligent capabilities are introduced and applied into ITSs over large-scale data sets trainings, which allow vehicles to make optimal decisions in tackling causal reasoning dynamic driving situations [5].

However, the introduction of causal AI-advanced technology into in-vehicle ITSs and autonomous driving algorithms has raised some concerns about their ability in completely eliminating the need for human intervention, especially during the transfer of crucial driving tasks to the in-vehicle central computer unit [6–8]. A valid option to tackle this is the introduction of non-causal reasoning techniques [9, 10], assimilating human behavior and integrating meta-knowledge to tackle sudden and recurrent changes in driving environment, e.g., when an unexpected (non-causal) situation takes place in front of the vehicle so one should drive cautious. In this respect, on-board ITSs should be able to take early actions in response to unexpected situations, imposing an adaptation of their behavior a priori, by predicting such future states and responding appropriately.

As driving decisions are time-sensitive, latencies could prove fatal for the safety ride of HAVs based on numerous causal and non-causal environment circumstances (i.e., inclement weather, complex terrain, transient environmental disturbances, unexpected on-road obstacles, forthcoming emergencies, etc.), [11]. In this respect, due to the ever increasing use of software for deploying silicon on chips enabling the coexistence of various autonomy levels, drivers should be able to inform the HAV, through their personal preferences towards driving automation aspects, how they want to be driven in order to increase their travel experience and comfort. In addition, HAV should be able to respond not only on causal reasoning effects, which depend on present and past inputs from the vehicle’s driving environment, but also on non-causal reasoning situations depending on future states associated with the complex driving scene. In this respect, both causal and non-causal reasoning effects affect the transition (downgrading or upgrading) between different levels of autonomy in HAVs.

According to the aforementioned specified problem, this study proposes an on-board cognitive management functionality, namely ‘CLoAS’ (Cognitive Level of Autonomy Selection), targeted at incorporating AI and non-causal reasoning techniques in responding quickly to changing environment situations and driver’s preferences, and therefore, enabling HAVs to operate each time in the best available LoA. More in detail, the proposed in-vehicle cognitive management functionality manages (i) data from sensors placed on HAVs, (ii) data from specific units of the road-side infrastructure via vehicular communications, (iii) driver’s personal preferences and profile data, (iv) previous knowledge and experience associated with the external causal environment, (v) non-causal reasoning effects associated with the intensely changing driving environment, and (vi) a computationally efficient decision making framework process, which evaluates the available information and automatically recommends the transition between different levels of autonomy according to changing environment situations and driver’s preferences.

The structure of the present paper is divided as follows: Sect. 2 describes the motivation and contribution of this work and Sect. 3 presents the background, through an overview in vehicle automation, vehicular communications, cognitive computing and non-causal reasoning effects. Section 4 describes in detail the architecture of the proposed ‘CLoAS’ architecture, whereas Sect. 5 presents the applied cognitive decision making approach. Section 6 contains indicative simulation results to showcase the efficiency of ‘the developed approach, whereas Sect. 7 provides conclusion remarks and plans for future research work.

2 Motivation and contribution

In the light of the above, the motivation for the present work is justified as follows: (a) several attributes/parameters which depend on present and future changing situations from the vehicle’s driving environment should be assessed and managed appropriately by the on-board ITSs, being able to adapt, fast and successfully, (b) several attributes/parameters related to driver’s personal preferences and his/her profile data should be assessed and managed appropriately by the in-vehicle ITSs, being able to support the interaction between drivers/users and HAVs, (c) non-causal reasoning effects on in-vehicle ITSs, which integrate meta-knowledge towards a complex driving environment, are still at a low level. In addition, the importance of the aforementioned attributes may specify the effective driving and interaction with HAVs. Therefore, an in-vehicle cognitive management functionality which combines cognitive decision-making analysis, causal learning situations, and non-causal reasoning effects, is a crucial on-board ITS for the effective driving of HAVs, being able to operate each time in the best available LoA.

The present study is significant, as it reports one of the first studies towards the introduction of a novel in-vehicle ITS, where non-causal reasoning situations associated with the meta-knowledge of the complex driving environment are taken into account for enhancing the cognitive management of LoA in HAVs. In particular, the contribution of the present study mainly lies in the following: (a) the design and implementation of an on-board ITS, which uses as input big data gathered by various sources, and provides drivers with the optimal LoA in a real-time automatic manner, (b) the identification and utilization of a hybrid (data-driven and event-driven) decision-making process, being able to operate each time in the best available LoA, improving thus the quality of road transportation, (c) the integration of non-causal reasoning techniques by handling emergency situations proactively, which can increase decision making speed and make LoA decisions faster, more reliable and more stable, and therefore, enhance the overall levels of travel safety.

3 Background

Vehicle automation technologies are being developed by the major automotive industries in transferring the critical driving tasks from a driver to an AI-operator system. The digitalization of tasks related to driving function aims to enhance safety and efficiency of on-road transportation activities, as well as to increase travel experience for the drivers [12, 13]. As automobile manufactures tend to design and produce more and more autonomously vehicles in the market [14], in-vehicle ITSs demand a high amount of reliable information towards vehicle’s state and it’s surrounding complex driving environment. In this direction, among others, HAVs need to be able to collect and recognize non-causal reasoning effects associated with the wider driving environment. These effects depend on future situations and states associated with the meta-knowledge of the complex driving environment [15].

Vehicular communications are expected to be one of the core elements towards newly-designed on-board ITSs, and thus, are moving us to increasingly intelligent cars. The main goal of vehicular communications is to establish communication networks in the whole transport area, including V2V (communications between vehicles), V2I (communications between vehicles and specific infrastructure units) and V2E (communications between vehicles and everything like pedestrians, cyclists, etc.) [16]. Thus, connected vehicles could then have the ability to communicate with other vehicles, as well as with specific parts of the transport infrastructure, e.g., traffic signs, traffic lights, etc. In addition, the embedded computer operator system of the HAV should integrate all the above kinds of communications, as well as crucial data from the external environment via various sources (external and internal sensors) [17, 18].

Moreover, any observed real-time traffic phenomena like road accidents, environmental disturbances, etc., can be sent by vehicles to the road-side infrastructure units for further dissemination. In this basis, when a connected vehicle senses an event, it sends an appropriate message, via a secure communication channel, to the nearby road-side infrastructure unit. The specific unit can disseminate this message to other vehicles in neighboring regions. As such, HAVs would be more aware towards the meta-knowledge information about a “future” driving scene and, therefore, can take early actions in response to unusual situations, being able to make appropriate informed and proactive decisions [19].

In the existing literature, commonly AI-related approaches like Support Vector Machines (SVMs), Artificial Neural Networks (ANNs), and Bayesian Networks (BNs) have been adopted in modeling intelligent driving platforms and systems by utilizing empirical data (present and past input) from various types of sensors in order to improve parameter learning and knowledge building [20, 21]. In this respect, to achieve different levels of autonomy under all types of driving environment situations, specified characteristics should be taken into account. First, the HAV’s central operator system must be a highly integrated AI system that can respond safely and without mistakes to varied driving scenarios of different characteristics. Second, the on-board operator system must be able to recognize and abstract the situational information contained in the external environment [22].

Causal analysis is essential for realizing the human-like driving scene understanding: it brings the ability to determine cause-effect relationships and provides a basis for reasoning about interventions, as well as what events might have happened differently, which are fundamental characteristics of human reasoning. On the other hand, it should be stated that the driving scene understanding usually goes beyond simple detection of persons and cars, and instead, masters overall contextual environment understanding. This includes non-causal reasoning, i.e., the integration of meta-knowledge about the scene (e.g., there is a school nearby so one should drive cautious) as well as complex scene related reasoning (e.g., a picture of a person that is printed on the side of a truck is not real). In this respect, non causal decision making forms the basis for well-performing, safe and reliable AI-enabled operator systems inside HAVs. As such, cognitive intelligence and non-causal decision making offer the ability to adapt quickly to external environment situations, e.g., an HAV must respond dynamically to what’s happening on the road [23].

To the best of our knowledge, it should be noted that the majority of studies in the existing literature has paid less attention in the simulation of non-causal statements in decision making algorithms. In this direction, an RCSD (Reduced-Complexity-Soft-Detection) scheme is presented, where decision feedback has been divided into causal and non-causal parameters to maximize the observation area, whereas a reasonable computational load is maintained simultaneously [24]. In a more recent study [25], a cognitive computing framework is proposed for enhancing higher levels of intelligence in autonomous driving, through empirical learning and intuitive reasoning, being able to improve the decision-making ability and adapt to complex driving environment scenes.

4 ‘CLoAS’ architecture

This section provides the system’s high-level architecture description, as well as the context which is envisaged to operate. As mentioned above, the majority of associated parameters like road condition, road type, non-causal situations in front of HAV, etc., can be changed dynamically. In this respect, the introduced ‘CLoAS’ functionality is intended to interact with the available in-vehicle driving automation levels enabling HAVs to operate each time in the best available LoA.

Similar architectures have been introduced in the past [24–26]. The present analysis builds upon these architectures and provides an architecture focusing on non-causal reasoning and better tailored for 5G infrastructures. In this respect, a three-layer architecture analysis is applied for ‘CLoAS’ functionality, as depicted in Fig. 1, which includes:

Figure 1
figure 1

‘CLoAS’ high-level architecture

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[i] driver layer, which is associated with: (a) Quality of Experience (QoE) driving automation parameters related to the behavior and performance of the in-vehicle AI-operator system (e.g., driver-HAV interaction, driver productivity, etc.), and (b) profile parameters related to the driver of the HAV (e.g., driving pleasure, driving experience, driving style, etc.).

[ii] sensory layer, which is associated with the collection of data from the real-time driving external surrounding scene by including (a) causal context acquisition (e.g., road type, road condition, level of vehicle congestion, etc.) and (b) non-causal context acquisition, (e.g., unexpected on-road obstacles, dynamic objects, etc.). Data aggregation is based on wireless sensors, which are placed on specific elements of the transport infrastructure (road signs, traffic lights, etc.) and on the connected vehicles. As such, vehicular networks can be formed between vehicles (moving objects) and parts of the infrastructure (static objects). It should be noted that measurements from sensors provide ‘CLoAS’ with data very often, so crucial input information is timely provided to ‘CLoAS’ functionality.

[iii] decision-making process layer which receives data from the sensor layer and the driver layer, and provides valuable decisions and corresponding actions. In addition, this layer uses two sets of policies, which are associated with the importance of input features. According to the first set of policies, driver’s preferences on predefined QoE automation parameters and predefined profile features are specified. To do so, each one of the above predefined parameters associated with the driver layer has a certain weight value with the anchors 0 (lowest importance) and 1 (highest importance). In this point, it should be stated that some input features related to driver layer could have the same importance, i.e., a driver may consider driver productivity and driving style equally important. Moreover, an additional set of policies is established as input in the decision-making process layer, which is associated with the external driving scene, as mentioned previously in the sensory layer. In a similar way, each one of the external environment features has a certain importance value (between 0 and 1) related to the HAV’s operator system. Such weight values may need to adapt frequently during the HAV’s ride, as external environment parameters (causal and non-causal) can be changed dynamically.

Furthermore, a knowledge and experience-based scheme is used as input in ‘CLoAS’ functionality, which supports the decision-making layer through two appropriate large-scale data sets. Such training data sets represent dependencies between input data and LoA selections. In particular, the first data set arises as a result of an evaluation process from the drivers regarding their level of satisfaction in using ‘CLoAS’ functionality in past road journeys. In general, this data set represents dependencies between QoE driving automation input parameters and LoA selections. In addition, the second data set represents dependencies between causal driving environment input data and LoA selections. The values of the second data set are obtained towards previous applications of the ‘CLoAS’ functionality through the AV’s in-vehicle operator system.

In addition, an appropriately structured database (data repository) is established, where all combinations of input features with the related decisions and actions are stored. Based on the above, whenever a specific scheme occurs as input in ‘CLoAS’, an initial search in previous cases is performed in the data repository by investigating one by one the list of the predefined input parameters. As such, the above procedure checks whether a similar input scheme has been addressed in the past via the comparison of the present input parameter values with previous running cases. If the similarity process is over a certain percentage, i.e., 95%, then the specific input scheme is considered as similar. Afterwards, ‘CLoAS’ seeks to find the decision-making solution, which has been applied to the similar incident, and whether this solution towards LoA prediction was “successful”. In this case, the decision-making algorithm does not need to run and the previous “successful” decision is applied again. On the other hand, the embedded algorithmic process in ‘CLoAS’ needs to run and take a “new” LoA decision, according to the procedure in the following Sect. 5.

Finally, a human interface layer, which offers useful information to the drivers regarding the applied LoA each time, should be implemented in ‘CLoAS’ high-level architecture. Let it be noted that human interface layer is of minor importance to the present study.

5 Decision making process

The present section describes the hybrid (data-driven and event-driven) process integrated in the ‘CLoAS’ functionality, as well as the usability of the proposed system, as depicted in Fig. 2. The present analysis has been based on past research efforts in modeling the process and optimization of reconfigurable and adaptive management functionalities, applied in the transportation field [4, 26–28].

Figure 2
figure 2

Proposed overall decision making process

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In this manner, the cognitive decision making process has been divided into two main parts, causal and non-causal. This separation has been introduced to maximize the observation window towards the complex and dynamic driving environment. In addition, for facilitating its operation, the overall process is divided into four main phases, as described below, aiming to maintain a certain level of simplicity (computationally intensive operations are undesirable in a real-time optimization system), without however compromising the effectiveness and extendibility of the proposed solution.

5.1 Causal context acquisition process

In modeling causal context acquisition of the overall decision making process in ‘CLoAS’ functionality, a supervised machine learning analysis (data-driven approach), based on the BNs theory, is provided because BNs have proven to be a valuable solution for representing causality and uncertainty in the road transportation domain [29]. This is justified due to the fact that BNs theory is a fast and accurate causal reasoning technique which is converging quickly, is easy to implement and no special infrastructure is needed.

Based on the above, as depicted in Fig. 3, a learning causal BN model is introduced, where its structure in known. The outcome (representing child node) of the proposed BN framework is variable LoA, which represents the on-board level of autonomy. In our analysis, three levels of autonomy (\(\mathrm{LoA}= 2, 3\) and 4) are assumed to be co-existed on-board in HAVs, based on the driving automation taxonomy provided previously in Sect. 3 (L2—partial automation, L3—conditional automation and L4—high automation).

Figure 3
figure 3

Proposed learning causal Bayesian framework

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In minimizing the complexity and maximizing the potentials of ‘CLoAS’ cognitive management functionality, the modeling of the causal context acquisition regarding (QoE) driving automation features and vehicle’s external causal environment is based on the introduction of the following six specified evidence features (representing parent nodes):

[a] road type (ROT) with the discrete reference states 1. village/rural road, 2. small urban road, 3. medium urban road (one line per direction), 4. big urban road (two lines per direction), 5. national road/highway

[b] road condition (ROC) with the discrete reference states 1. snowy and windy, 2. foggy, 3. wet/slippery, 4. with abnormalities, 5. good

[c] vehicle congestion level (VCL) with the discrete reference states 1. extremely high, 2. quite high, 3. average, 4. quite low, 5. extremely low

[d] driving pleasure (DPL), driver productivity (DPR) and vehicle-environment interaction (VEI) with the discrete reference states 1. extremely low satisfaction, 2. quite low satisfaction, 3. average satisfaction, 4. quite high satisfaction, 5. extremely high satisfaction

According to BNs theory, learning task includes the estimation of conditional probabilities for the aforementioned parameters (ROT, ROC, VCL, DPL, DPR, VEI). Each input node is associated with its relative Conditional Probability Table (CPT), which includes three columns as three levels of autonomy are assumed to be co-existed on-board, and five lines due to its predefined discrete reference states. Indicatively, Fig. 4 depicts the CPT structure for the “DPR” input variable.

Figure 4
figure 4

Structure of a CPT focusing on “DPR” variable of interest

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Each cell in the CPT provides a probability value, i.e., the conditional probability \(\operatorname{Pr}[V_{\mathrm{DPR}} = rv_{\mathrm{DPR}} ^{2} | \mathrm{LoA} = 3]\) states on how probable it is that variable “DPR” will obtain a particular reference state “\(rv_{\mathrm{DPR}}^{2} = 2\) (quite low satisfaction)”, taking into consideration that “\(\mathrm{LoA}= 3\) (conditional level of autonomy)” has been selected. On this basis, by addressing a specific level of autonomy, the most probable reference state that is achieved for the “DPR” variable is the one related to the maximum Pr.

In modeling the above, an appropriate reconfiguration and adaptation learning strategy is implemented, which aims to maximize the conditional probabilities for the aforementioned specific causal variables of interest (ROT, ROC, VCL, DPL, DPR, VEI). Such a procedure helps ‘CLoAS’ functionality to gradually obtain knowledge and experience. In this respect, large-scale data sets are used, as mentioned previously in Sect. 4, which help conditional probabilities to be updated.

More in detail, in the present analysis, BN parameters were estimated using a supervised data-driven machine learning method, based on Naïve-Bayes (NB) classifier. Such a technique assumes that the BN parameters are conditionally independent of each other. It has been stated that the aforementioned approach, even when the assumption of independence between BN parameters does not hold, shows good performance in classification accuracy problems [30, 31]. According to NB classifier, a Probability Function (PF) should be defined, which states on how probable it is that a specific input scheme can be achieved, taking into consideration that a specific LoA has been selected:

$$\begin{aligned} {\mathrm{PF}}_{i} = \Pr [ {\mathrm{LoA}} = i ] \bullet \prod _{j = 1}^{6} \Pr \bigl[ {V}_{ {j}} = {rv}_{ {j}}^{ {k}} | {\mathrm{LoA}} = {i} \bigr]. \end{aligned}$$
(1)

In (1), prior probabilities \(\operatorname{Pr}[\mathrm{LoA}= i]\) are calculated based on the volume of existing data for each LoA (\(i= 2, 3, 4\)) according to the collected large-scale data sets. It is obvious that the sum of all the \(\operatorname{Pr}[\mathrm{LoA}= i]\) values equals to one. The above underlines that as more information is existed on each available LoA, more reliable knowledge is achieved, and thus, \(\mathrm{PF}_{ {i}}\) values become higher.

According to (1), \(\mathrm{PF}_{ {i}}\) values are updated based on the calculation of the conditional probabilities \(\operatorname{Pr}[V_{ {j}}= rv_{ {j}}^{ {k}} | \mathrm{LoA} = i]\), where \(rv_{ {j}}^{ {k}}\) denotes the k-th reference value (\(k= 1, 2, 3, 4, 5\)) for the j-th parameter (ROT, ROC, VCL, DPL, DPR, VEI), when a specified state i of variable LoA occurs. The present learning process is based on the absolute difference of the mean collected value \(v_{ {j}}^{\mathrm{coll}}\) (extracted from the relative large-scale data sets) from the reference state \(rv_{ {j}}^{ {k}}\). To do so, the following correction factor, \(\operatorname{cor} _{ {j}}^{ {k}}\), can be defined as follows:

$$\begin{aligned} \operatorname{cor}_{j}^{k} = 1 - \frac{ \vert rv_{j}^{k} - v_{j}^{ {\mathrm{coll}}} \vert }{rv_{j}^{5} - {r}v_{j}^{1}}, \quad k = 1, 2, 3, 4, 5. \end{aligned}$$
(2)

The factor \(\operatorname{cor} _{ {j}}^{ {k}}\) can take values between 0 and 1. Value 1 states that reference state \(rv_{ {j}}^{ {k}}\) is closed to \(v_{ {j}}^{\mathrm{coll}}\). In such case, the corresponding conditional probability value \(\operatorname{Pr}[V_{ {j}}= rv_{ {j}}^{ {k}} | \mathrm{LoA} = i]\) should be reinforced. Based on (2), the correction of the CPT values can be calculated as below:

$$\begin{aligned} &\Pr \bigl[ {V}_{ {j}} = {rv}_{ {j}}^{ {k}} | { \mathrm{LoA}} = {i}\bigr]_{ {\mathrm{new}}} \\ &\quad = {L}_{ {j}} \cdot { \operatorname{cor}}_{ {j}}^{ {k}} \cdot \Pr \bigl[ {V}_{ {j}} = {rv}_{ {j}}^{ {k}} | {\mathrm{LoA}} = {i} \bigr]_{ {\mathrm{old}}}. \end{aligned}$$
(3)

In (3), the factor \(L_{ {j}}\) is used to guarantee that all the “new” conditional probability values sum up to 1, and can be calculated as follows:

$$\begin{aligned} {L}_{ {j}}\sum_{ {j} = 1}^{6} { \operatorname{cor}}_{ {j}}^{ {k}} \cdot \Pr \bigl[ {V}_{ {j}} = {rv}_{ {j}}^{ {k}} | {\mathrm{LoA}} = {i} \bigr]_{ {\mathrm{old}}} = 1. \end{aligned}$$
(4)

Based on the above, it can be defined that the proposed supervised (data-driven) machine learning method converges when the corresponding conditional probability related to reference state \(rv_{ {j}}^{ {k}}\), which is closest to \(v_{ {j}}^{\mathrm{coll}}\), becomes the highest. Furthermore, it should be stated that although the above procedure takes into account six input causal parameters, the architecture design of the aforementioned learning strategy is highly scalable. On this basis, it can be easily adapted so as to introduce additional variables in modeling the causal context environment.

5.2 Non-causal context acquisition process

As mentioned in Sect. 4, vehicular networks play the main role for increasing the cognitive features of ‘CLoAS’ functionality through non-causal effects and event-driven process. In this case we take advantage of the fact that when vehicular networks sense a future (non-causal) incident a few kilometers in front of the AV, like a random and non-deterministic movement of an object across the road, they send that information to its central on-board operator system, so it can expand this meta-knowledge in making optimal proactive decisions towards LoA prediction.

In order to model the above aspect, we assume that the in-vehicle computer system receives such a message about a non-causal incident, namely “Non-Causal Situation (NCS)”, and computes a normalized value \(\mathrm{norv}_{\mathrm{NCS}}^{ {i}}\) for each LoA (\(i= 2, 3, 4\)). It holds that:

$$\begin{aligned} {\mathrm{norv}}_{ {\mathrm{NCS}}}^{i} = \frac{rv_{m}^{i}}{5}, \end{aligned}$$
(5)

assuming that \(rv_{ {m}}^{ {i}}\) denotes the m-th reference value among a set of five discrete levels, \(m= 1\) (very low), \(m= 2\) (quite low), \(m= 3\) (average), \(m= 4\) (quite high), and \(m= 5\) (very high), for each state i of variable LoA. In this respect, each level m represents the reaction degree of LoA in tackling NCS. It is obvious that more accuracy is added to non-causal context acquisition process in case the number of reaction levels increases. It should be stated that as the reaction degree of LoA in tackling NCS becomes lower, normalized value \(\mathrm{norv}_{\mathrm{NCS}}^{ {i}}\) takes a value close to zero.

5.3 Evaluation analysis

The overall decision making process produces its output based on the above mentioned processes related to causal and non-causal context environment. For reaching the classification outcome, a total objective function (OFtotal) can be defined for each LoA (\(i= 2, 3, 4\)):

$$\begin{aligned} {\mathrm{OFtotal}}^{ {i}} = {\mathrm{OFc}}^{ {i}} + {\mathrm{OFnc}}^{ {i}}. \end{aligned}$$
(6)

The first term (\(\mathrm{OFc}^{ {i}}\)) is associated with the causal context acquisition, and can be defined for each LoA (\(i= 2, 3, 4\)) as follows:

$$\begin{aligned} {\mathrm{OFc}}^{ {i}} = \sum_{j = 1}^{6} \bigl\{ \max ( {\mathrm{PF}}_{i} ) \bigr\} .w_{j}. \end{aligned}$$
(7)

According to (7), the calculation of \(\mathrm{OFc}^{ {i}}\) relies on the importance (weight values \(w_{ {j}}\)) for each causal BN parameter j (ROT, ROC, VCL, DPL, DPR, VEI), based on driver’s personal preferences and operator system policies.

The second term (\(\mathrm{OFnc}^{ {i}}\)) is based on the normalised values calculated in (5), by taking into consideration the non-causal context acquisition, as well as the corresponding weight value \(w_{\mathrm{NCS}}\). In this manner, \(\mathrm{OFnc}^{ {i}}\) can be computed for each state i of variable LoA through the following formula:

$$\begin{aligned} {\mathrm{OFnc}}^{ {i}} = n {\mathrm{orv}}_{ {\mathrm{NCS}}}^{ {i}}.w_{ {\mathrm{NCS}}}. \end{aligned}$$
(8)

According to (8), as the value of \({\mathrm{norv}}_{\mathrm{NCS}}^{ {i}}\) becomes higher, the \(\mathrm{OFnc}^{ {i}}\) value increases, and therefore, a high degree of reaction is depicted for the level of autonomy i (\(i= 2, 3, 4\)). In total, the available levels of autonomy are classified according to OFtotal values, and the one with the highest value is selected by ‘CLoAS’ functionality.

6 Case study and discussion

This section showcases the performance of the applied decision making process in ‘CLoAS’ management functionality through an indicative discrete-event simulation analysis.

6.1 General aspects

A discrete-event simulation analysis based on SimEvents [32] is being applied to validate the efficiency of the aforementioned hybrid decision making process, mostly in terms of speed of convergence and accuracy. In this respect, an indicative case study is assumed, where a human driver desires to have a road journey with his/her HAV (owned or shared).

First of all the driver needs to log on ‘CLoAS’ management functionality, which may be part of an integrated in-vehicle central platform. When the driver enters ‘CLoAS’ for the first time, he/she has the ability to complete a data-based form towards his/her personal preferences regarding a predefined group set of QoE driving automation parameters, as well as his/her profile characteristics (driving pleasure, driving style, driving experience, etc.). If the driver has already registered, ‘CLoAS’ functionality recognizes him/her. In such case, the driver has access to his/her personal preferences, past activities and profile characteristics. At the same time, the HAV’s on-board operator system specifies the importance (weight values) given to a predefined group of external causal environment features (ROT, ROC and VCL in our case).

As mentioned above, the main goal of the proposed hybrid algorithmic process in ‘CLoAS’ functionality is to interact with the un-vehicle levels of autonomy group, and take reliable decisions towards the best available LoA, based on the collected data from the sensor and driver layers. In any case, the driver of HAV is notified accordingly with the implementation of the proposed LoA, though the interface system of ‘CLoAS’.

6.2 Case study

The present scenario aims to provide evidence on the efficiency of ‘CLoAS’ management functionality, by enabling HAV to operate each time in the best available LoA. The simulation process for this case study is applied in 30 series of discrete runs (number of computation count) every 0.45 msec. Therefore, the total response time is 13.5 msec, which is essentially lower than the usual latencies confronted in 3G, 4G and 5G mobile communication infrastructures. In this respect, the proposed solution can be applied under any underlying existed communication protocol.

More in detail, driver John is considered. John has already registered on ‘CLoAS’ in the past, where his personal preferences regarding QoE driving automation features (DPL, VEI and DPR in our analysis) and his profile characteristics have been stated. According to Table 1, driver John gives a high importance (0.3) for DPL and VEI parameters, while he has less interest (0.15) in DPR parameter. In this manner, John disposes a unique identity for ‘CLoAS’.

Table 1 Input parameters, collected enaluation values and respective weights
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John desires to move on with his HAV from A (represents starting point SP) to B (represents destination point DP), on a well-maintained big urban road (two lines per direction), with a quite low vehicle congestion level, as depicted in Fig. 5. As shown in Table 1, according to the external causal environment acquisition, parameter ROC has a low importance weight value (0.05) for the in-vehicle computer system, whereas ROT and VCL causal parameters have higher importance (0.1) according to road type (big urban road) and vehicle congestion level (quite low) settings. It is obvious that all the weights have a sum equal to 1, due to the fact that initially there are six input parameters.

Figure 5
figure 5

Case study description

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At point C, a message for a non-causal situation (random and non-deterministic movement of an object across the road), a few kilometers in front of the HAV, is gathered from a specific road-side infrastructure unit via an appropriate V2I communication link. Therefore, after point C, seven input (causal and non-causal) parameters should be considered in total. At the same time, as shown in Table 1, the on-board computer system gives a very high importance value (0.3) to the non-causal situation NCS due to its quite high danger level. In addition, due to the fact that the sum of weights regarding all the input (causal and non-causal) parameters should remain again equal to 1, the weight values towards QoE driving automation parameters have been adjusted appropriately. At this point, it should be stated that the weight factors for the causal external environment parameters (ROT, ROC and VCL) remain the same like previously.

Decision making process (applied at the beginning): Initially, the conditional probabilities \(\operatorname{Pr}[V_{ {j}}= rv_{ {k}}| \mathrm{LoA} = i]\) are equal to 0.2, as no previous knowledge is available to ‘CLoAS’. Furthermore, the present simulation assumes that the prior probabilities \(\operatorname{Pr}[\mathrm{LoA}= i]\) are equal to 0.33 for the three levels of autonomy, due to the assumption that an equal volume of information exists for each level of autonomy, according to large-scale data sets already mentioned in Sect. 4.

By applying the aforementioned learning strategy, as described in Sect. 5, the distributions of conditional probabilities for two QoE driving automation features (DPR, VEI) regarding \(\mathrm{LoA}= 4\) (high level of autonomy), are shown in Figs. 6(a) and 6(b), respectively. In these graphs, the horizontal axis denotes the number of calculations (discrete runs) where the proposed machine learning process conducts computations.

Figure 6
figure 6

Discrete-time variations of conditional probabilities for the QoE driving automation parameters (a) DPR and (b) VEI regarding the high level of autonomy (\(\mathrm{LoA}= 4\))

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The above figures show that the applied learning strategy in ‘CLoAS’ readily learns the capabilities of the parameters DPR and VEI to reach specific reference states (after almost 18 discrete simulation steps), and therefore, to converge to the mean collected values (4.7 and 4, respectively) towards \(\mathrm{LoA}= 4\) (high level of autonomy). For example, with respect to the parameter DPR (Fig. 6(a)), the probability \(\operatorname{Pr}[V_{\mathrm{DPR}}= 5 | \mathrm{LoA} = 4]\) takes very soon much higher values than the probability \(\operatorname{Pr}[V_{\mathrm{DPR}}= 4 | \mathrm{LoA} = 4]\) with respect to the “neighboring” reference state. In addition, there is a slight degradation for \(\operatorname{Pr}[V_{\mathrm{DPR}}= 3 | \mathrm{LoA} = 4]\), whereas a severe diminishment for the two remaining conditional probabilities \(\operatorname{Pr}[V_{\mathrm{DPR}}= 2 | \mathrm{LoA} = 4]\) and \(\operatorname{Pr}[V_{\mathrm{DPR}} = 1 | \mathrm{LoA} = 4]\), is existed. It should be stated that similar curves can also be depicted for \(\mathrm{LoA}= 2\) and \(\mathrm{LoA}= 3\).

Furthermore, the proposed decision-making algorithmic process decides on \(\mathrm{LoA}= 4\) as the most suitable to be applied initially. The above decision is based on the calculation of the objective function values (OFc), through (7), for the three available driving automation levels, as shown in Fig. 7, by taking into account six specified parameters (ROT, ROC, VCL, DPL, DPR, VEI), their input values, and policy information. The above results demonstarte, in general, that a small number of discrete computations (runs) is used for making decisions towards the best available LoA.

Figure 7
figure 7

Objective Function values (OFc) for all the available in-vehicle levels of autonomy (\(\mathrm{LoA}= 2, 3\) and 4) at the beginning

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Decision making process (applied at point C): In this phase, the effect of non-causal reasoning in adapting the vehicle’s LoA is presented though the applied algorithmic process. As mentioned previously, at point C, a message for a non-causal situation NCS at point D, a few kilometers in front of the HAV, is gathered from a specific road-side infrastructure unit via an appropriate V2I communication link. As mentioned previously, after the receipt of the message, the in-vehicle computer system gives a high weight value (0.3) regarding the non-causal parameter NCS, as depicted in Table 1, and therefore, informs ‘CLoAS’ for the new change in driving environment.

Furthermore, the values representing the level of response for each LoA towards NCS are presented in Table 1. In this manner, the partial level of autonomy (\(\mathrm{LoA}= 2\)) is assumed to be able to response at a quite high level (\(rv_{ {m}} = 4\)) towards the non-causal parameter NCS, leading to a high normalized value \(\mathrm{norv}_{\mathrm{NCS}}= 0.8\). In addition, the other in-vehicle levels of autonomy (conditional and high) show a lower reaction degree regarding NCS.

Based on the above, at point C, only a few microseconds after the receipt of the non-causal situation, the above decision making algorithmic process needs to run again by catching the non-causal situation in HAV’s vicinity and reaching a decision towards the ‘new’ LoA. In this case, the corresponding objective function values (OFtotal) have been executed for the available driving automation levels and are shown in Fig. 8. The decision making algorithm decides on \(\mathrm{LoA}= 2\) (partial level of autonomy) as the most suitable to be applied (at point C) by considering seven specified (causal and non-causal) parameters (ROT, ROC, VCL, DPL, DPR, VEI, NCS), their input values, as well as the relative policies.

Figure 8
figure 8

Objective Function values (OFtotal) for all the available in vehicle levels of autonomy (\(\mathrm{LoA}= 2, 3\) and 4) at point C

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The above results demonstrate, in general, that a small number of discrete calculations is used for making decisions regarding the best available LoA by catching the new evidence (non-causal situation NCS) in driving environment.

7 Conclusion remarks and future work

Highly HAVs are expected to improve the performance of terrestrial transportations by providing safe and efficient travel experience to drivers and passengers. On-board cognitive management systems are a promising approach towards enhancing the travel experience with HAVs by responding to the complexity of driving environment. The main mission of such systems is to tackle sudden and recurrent changes in the vehicle’s external environment by dynamically reconfiguring the embedded algorithms and features they use. Furthermore, the introduction of non-causal reasoning situations, by incorporating meta-knowledge effects related to a complex driving environment, imposes better adaptation of AV’s behavior in predicting such future states and responding appropriately.

In the light of the above, the present study proposes an on-board cognitive management functionality, namely ‘CLoAS’, which collects data from various sources and applies a hybrid (data-driven and event-driven) algorithmic process for obtaining each time the best available LoA, when a driver desires to have a travel journey with his/her HAV. Compared to other similar functionalities, which have been introduced in the past, the ‘CLoAS’ architecture is: (a) modular, (b) scalable, (c) with modernized components and (d) encompassing a first ever non causal reasoning module compared to today’s other cognitive management approaches with respect to the effective operation of HAVs. In general, the simulation results show that the proposed ‘CLoAS’ functionality can provide proactive and reliable actions, based on previous knowledge for causal reasoning environment features, as well as on meta-knowledge for non-causal reasoning effects.

The present study has some notable limitations. First of all, there are specific driver’s personal preferences and certain environment characteristics within the driving scene, where the functionality’ response has been tested, and therefore, the generalization of the results is hindered. In addition, the overall decision-making analysis, which helps ‘CLoAS’ gradually obtain knowledge, is based on the NB classifier supervised machine learning method, where the input variables (ROT, ROC, VCL, DPL, DPR, VEI), which cause the random variable LoA, are assumed to be statistically independent. In this respect, the followed knowledge-based learning process maintains a certain level of simplicity in proactively identifying the optimal LoA, in terms of accuracy and speed of convergence. Moreover, the weight values of all the input parameters (ROT, ROC, VCL, DPL, DPR, VEI, NCS) were taken randomly without relying on any assumptions or/and any other evidences.

Last, the present analysis could be extended to a series of work areas. On this basis, the potential to change dynamically and automatically the importance (weight values) attributed to the input parameters, and then testing the functionality’s response, could also be investigated. Additionally, further supervised machine learning techniques could be applied to the decision making analysis of the proposed ‘CLoAS’ in obtaining the appropriate decisions. Furthermore, due to the fact that ‘CLoAS’ functionality involves high-level shared control and interaction of vehicle intelligence with the human driver, real-field tests and simulations should be implemented to showcase the efficacy of the developed approach. Moreover, what could be also investigated, is the potential to run additional driving scenarios and simulations (e.g., no equal volume of information exists for the available levels of autonomy) to further enhance the validity of correctness/accuracy of the developed approach, helping a lot to obtain even more encouraging results. In addition, what could also be part of our future research activities, is how the proposed ‘CLoAS’ functionality can be integrated into a seamless autonomous driving intelligence by interacting with perception/computer vision systems.