Hierarchical Diagnostics and Risk Assessment for Energy Supply in Military Vehicles

Abstract

Hybrid vehicles are gaining increasing global prominence, especially in the military, where unexpected breakdowns or even power deficits are not only associated with greater expense but can also cost the lives of military personnel. In some cases, it is extremely important that all battery cells and modules deliver the specified amount of capacity. Therefore, it is recommended to introduce a new measurement line of rapid diagnostics before deployment, in addition to the usual procedures. Using the results of rapid testing, we recommend the introduction of a hierarchical three-step diagnostics and assessment procedure. In this procedure, the key factor is the building up of a hierarchical tree-structured fuzzy signature that expresses the partial interdependence or redundancy of the uncertain descriptors obtained from the rapid tests. The fuzzy signature structure has two main important components: the tree structure itself, and the aggregations assigned to the internal nodes. The fuzzy signatures that are thus determined synthesize the results from the regular maintenance data, as well as the effects of the previous operating conditions and the actual state of the battery under examination; a signature that is established this way can be evaluated by “executing the instructions” coded into the aggregations. Based on the single fuzzy membership degree calculated for the root of the signature, an overall decision can be made concerning the general condition of the batteries.

1. Introduction

Lithium-based batteries are gaining ground with the proliferation of electric vehicles [1,2]. Today, Li-ion batteries can be found everywhere due to their reliability and high energy density, ranging from the automotive, water, and aviation industries to the military [3,4]. Due to their widespread use and different manufacturing methods, not all batteries should be used for the same purpose. They act as an energy store in all cases, but there are different temperature and performance requirements in entertainment or industrial devices, and others still in automotive applications. Batteries used when in traffic must also comply with special safety conditions; therefore, many aspects need to be considered when designing the system [5,6,7]. Furthermore, during their use, various risk analyses are performed on them [8,9]. The use of batteries in the military has long been of interest, with several publications addressing the topic [10,11].

Due to recent changes in requirements, battery diagnostic and testing procedures have lately undergone significant development [12,13]. Several old and new diagnostic procedures can be observed in the literature for both system disassembly and non-disassembly methods. The most accurate condition estimates are obtained by disassembly tests, which examine the structure of the battery. Such procedures include CT [14,15], ultrasonic [16], or surface digitization (DIC) [17,18,19] methods. The disadvantage of these solutions is that they require the disassembly of the battery system, which is a slow and complicated procedure. It may also void the warranty of the vehicle. Therefore, in the case of non-self-developed systems, it is advisable to choose a non-disassembly method by which a continuous condition survey can be achieved. These processes can be further divided into tests, based on the test type, which can be distinguished by direct and computational methods [20]. Direct methods (based on tests) usually require intervention: discharge tests [21], battery open circuit voltage tests [22], internal resistance measurement [23], hybrid pulse tests, and power characterization [24]. The advantage of these methods is that the condition of the system is examined, based on data from real measurements—in most cases, very accurately. Their disadvantage is that they are not always feasible and that the information about the condition of the battery is obtained only at the given measuring point. A full discharge test is required to analyze the full range, which is time-consuming. Therefore, in most cases, it is necessary to use different estimation procedures (calculation methods). In the calculation methods, the battery parameters (SOC—state of charge, SOH—state of health) are estimated using different algorithms [25,26,27]. Some of these are highlighted: coulomb counting [28], modified coulomb counting [29], statistical approaches [30,31], hybrid methods [28], machine learning [32,33,34], and degradation pattern recognition with transfer learning [35].

Battery maintenance is usually provided by the manufacturers, but there are also international standards and recommendations [22,24]. The test procedure we propose is a combination of these methods. On the one hand, we use built-in estimation methods (SOC, SOH), which are tested periodically. On the other hand, we also examine the condition of the cells using real measurements, wherein we search for faulty cells using statistical methods. However, the use of capacity calculation and statistical methods, and the introduction of machine learning methods, will be essential for long-term efficient use.

Prolonged storage, transport, or large temperature changes can cause high-capacity degradation [36,37]. In order to establish that the expected value is fully met in all cases, tests are required. In some military scenarios, however, it is especially important to have the most accurate information on the condition of the batteries as soon as possible after commissioning. Therefore, it is important to introduce a rapid test procedure.

The focus of our article is on the following points: Section 2 describes the benefits of using ground hybrid military vehicles and details those types of military vehicles that will be more efficient with hybrid propulsion, after which the section explains the possible maintenance systems and strategies of hybrid military vehicles and introduces the importance of battery management systems for the maintenance of hybrid military vehicles.

In Section 3, we present our proposed novel 3-step battery diagnostic procedure. The starting point of this method is a fast test procedure, shown alongside an analysis of its usability when real measurements are available.

In Section 4, we present the build-up of the hierarchical risk assessment model, based on the rooted tree graph-structured fuzzy signatures. The hierarchical structure here expresses the mutual interdependencies of the measured but uncertain (and, thus, fuzzy) features. The aggregation operations help evaluate the combinations of these uncertain descriptor values. Through an evaluation of the entire fuzzy signature, by calculating the resulting value assigned to the root, the fuzzy decision process of 3-step battery diagnostics may be completed.

The efficiency of the procedure was tested by first measuring the battery system of a fully electric vehicle (see Section 5) as the EV mode of hybrid military vehicles is fairly close to such a vehicle’s behavior.

In the last section, we briefly summarize our results and present the possibilities for further development.

The advantage of the method we propose is that it is not only the built-in factory estimation algorithm that must be used to decide whether a vehicle is suitable for use or not. Another advantage of this method is the classification system and the error search method, with the help of which the weak points of the system can be determined per module, thus facilitating faster repair and replacement.

2. Hybridization of Military Vehicles

A hybrid military vehicle is a vehicle that is used for the transportation of equipment for combat purposes or for accomplishing a military operation in silent or stealth mode. Custom-designed for the armed forces, they are almost invariably armored and, thanks to the electronic and mechanical equipment installed, can be driven over difficult terrain.

2.1. Ground Hybrid Military Vehicles

Ground hybrid military vehicles include military civil engineering machines, which are used in military areas to carry out construction work. These include, among others, mine clearance and excavation machines, vehicles for crane work, and mining machines. Light tactical vehicles can be used for weapons transport, management and control tasks, reconnaissance and rescue, and tactical missions. Military light commercial vehicles are four-wheel-drive vehicles that are designed specifically for military purposes. They are mainly used by the military to transport soldiers, weapons, and supplies, and to evacuate wounded soldiers. They are designed for speed, good maneuverability, and military capabilities (weaponry). Tanks are armored, tracked military vehicles with armaments mounted in a so-called turret. They are designed to provide adequate armor protection, high maneuverability, and sufficient speed, which are all essential on the battlefield.

Hybrid vehicles are of increasing significance in the world, especially in the military. The basic feature of series hybrid military cars is that they use an internal combustion engine to drive a generator, which supplies electricity to the battery and the electric motor(s). The hybrid military vehicles are particularly efficient, being equipped with a high-capacity battery that ensures quiet operation and a long range. For the soldiers, the stealth mode of hybrid military vehicles gives a tactical advantage in military operations as they can launch surprise attacks. The electric drive can increase the acceleration data and the vehicle can hide from infrared heat sensors when in battery mode. When using an electric motor, the vehicle has lower heat and noise emissions. Hybrid military vehicles can serve an increased number of electrical loads (on-board systems, weapons, radar, and radio communication equipment) with generators. An important objective is to optimize the use of space so that batteries and electric motors take up minimal space in the passenger compartment and luggage trunk. In the case of hybrid powertrains, it is particularly important to monitor the instantaneous properties of the installed battery. The condition-monitoring system of the battery provides various diagnostic methods. The diagnostic capabilities ensure the operability and increased reliability of the hybrid-military vehicle over the long term. Any changes to the parameters of the battery affect the operation and efficiency of the hybrid drive system, so battery testing and condition monitoring are of particular importance.

2.2. RST-V Series Hybrid Military Vehicle

In the case of the RST-V hybrid armored military vehicle developed by Falls Church, a 2.5 L diesel engine drives a 110-kW generator, which supplies power to the 20 kWh Li-ion battery and to four one-by-one 50 kW electric motors, one located on each wheel. The on-wheel motors also significantly reduce the risk of the vehicle overturning and help to maintain stability.

The army often sets up temporary military bases that are far from utility networks. The generators, which are part of the propulsion system, can provide electricity for high-powered computers and medical support machines that previously required heavy and noisy auxiliary generators.

2.3. Hybrid Military Vehicle Maintenance Systems

The type of chosen maintenance strategy is of paramount importance to avoid breakdowns in hybrid military vehicles. Unexpected breakdowns are not only associated with higher costs but can also cost the lives of soldiers when a military or disaster-relief SUV becomes inoperable on the battlefield. We introduce some successful service techniques that are likely to help avoid surprise breakdowns.

2.4. CMMS—Computerized Maintenance Management System

During the functioning of the CMMS maintenance system, failure data is used to detect the common failure modes. In the military, the failure of the caterpillar track is one of the critical factors, as it renders the vehicle completely unroadworthy. One of the main causes of failure is excessive wear; the basic components of wear are the normal operational load, the specific wear, and the traveled distance. The surface, temperature, and composition of the terrain are the primary determinants in terms of maintenance.

As an example, the multiplication factors for the different road surfaces are summarized in

Table 1. Multiplication factors of road surfaces.

Surface Type	Multiplication Factor
Paved road	2.00
Unpaved road	1.00
Light terrain	1.00
Medium terrain	1.25
Heavy terrain	1.50
Roughness of Terrain	Multiplication Factor
Flat	1.00
Hilly	1.25
Mountainous	1.50

, and are essential for determining the life expectancy of the caterpillar tracks.

Likewise, the operational conditions and circumstances of the energy supply systems, batteries, should also be taken into consideration, parallel with the actual status that has been recorded regularly and on the spot before deployment (see Section 5). The values of SOC and SOH of the battery are two of the most important key input parameters of a computerized maintenance management system. The monitoring of these values is essential to preserving battery capacity and lifetime.

2.5. FMEA—Failure Mode and Effect Analysis

The monitoring sensors and transducers are integrated into hybrid military vehicles to prevent failures. The operating characteristics are tested at certain intervals by dedicated measuring and monitoring devices, depending on the type of equipment, manufacturer, or operator. The process involves the use of modern testing and diagnostic techniques, such as vibration analysis, thermography, analyses of engine parameters, and the analysis of lubricant quality. The constant monitoring of operating factors ensures the detection of the onset of a fault and the identification of the location and type of the anomaly. The battery diagnostics software and solutions that are used in hybrid military vehicles contribute to fault detection and help in the completion of necessary maintenance.

2.6. RCM—Reliability-Centered Maintenance

RCM-based technology is primarily used in military maintenance systems. Similar to the FMEA method, it is based on an examination of the functioning of components, in order to avoid potential failures and preserve the original function of the devices. The strategy analyzes failures according to statistical principles and calculates the probability and the expected timescale of failure, using conditional probability over the lifetime of the vehicle.

The maintenance and diagnostics processes of hybrid military vehicles are facilitated by battery-monitoring systems. The battery-monitoring systems contribute to the maintenance of hybrid military vehicles, with the help of the different control algorithms and condition-monitoring technologies and sensors. Section 3 describes a new approach for the RCM maintenance system, which is well suited for battery testing and condition monitoring. The new methodology ensures more efficient diagnostics of systems and allows more accurate analyses. The new strategy includes important innovations and reflects a new approach that is described in detail in Section 3.

3. Battery System-Testing Opportunities with Three-Step Diagnostics

Newly purchased systems work well and reliably for a long time, but there may be a point at which individual modules start to age rapidly. In this case, either the entire system needs to be replaced or some modules can be changed. Replacement of the entire system is more common when the modules continue to age equally. However, in a rapid deployment scenario or in urgent circumstances, there is no time to constantly replace the entire system and, in some cases, replacing a module (or cell) can solve the problem. Furthermore, during long-term deployments or military exercises, the continuous delivery of multiple systems is not possible. Therefore, a fast and accurate battery diagnostic procedure needs to be developed.

As it is not always possible to perform specialized time-consuming measurements during deployments, it is advisable to plan only short additional confirmatory tests, which are suitable for rapid condition assessment. Therefore, it is necessary to carry out maintenance and condition tests at regular intervals before relocating. However, in some cases, it is extremely important that all cells and modules deliver at least the specified minimum amount of capacity, otherwise, the vehicle may become immobile even in a critical situation. Therefore, the introduction of a new measurement strategy, rapid diagnostics, is recommended, in addition to the usual procedures.

Based on these considerations, we recommend the introduction of three-step diagnostics. The preliminary and most important step is to provide each pack of the most easily replaceable units (in some cases a cell, mostly a module) with a unique identifier.

The first diagnostic step is continuous data backup and analysis at the battery cell level, based on telemetry data (SOC and SOH, max-min cell, cell deviation, etc.) Based on the results of the continuously assembled cell data and built-in estimators (SOC, SOH), each module receives a criticality factor, as with road vehicles, with the additional proviso that the condition of each cell is monitored separately.

The second step is to use periodic battery maintenance, e.g., inspecting the current condition every six months, or refining the telemetry data and built-in estimators.

The third and final step is the rapid test procedure, in which it is recommended to develop a special acceleration and deceleration concept for the period from 60 s to 600 s. With this method, we examine the differences between the cells in the entire system and filter out any faulty, weaker cells. During this time, it is possible to examine whether the batteries have been damaged during storage, transport, and assembly. However, it is not a suitable method for testing batteries in a critical range. One such critical range is a high current load at low charge levels (e.g., uphill). It is important to note that frequent heavy-duty testing has a lifetime detrimental effect and should only be performed during periodic battery maintenance. Furthermore, when performing a rapid test procedure, care must be taken to use as little energy as possible, so as not to have a significant effect on the range.

The aim of the tests is to determine a new data collection and classification methodology that can give a sufficiently accurate guide to battery condition, even in data-poor cases. After evaluating the results, it is recommended to use the following classes:

• Suitable for military use (90–100%);
• Suitable for short-term military deployment (80–90%);
• Suitable for civilian use only (70–80%);
• Recommended for reuse (40–70%);
• Waste (0–40%).

The values in parentheses indicate the SOH of the battery as a percentage, wherein 100 is the best value. It is recommended that the rating be displayed on each module and updated on an ongoing basis.

In the following chapters of our paper, we examine the results obtained during the rapid tests and their important factors for risk analysis with real measurements.

4. Hierarchical Risk Assessment at Batteries

By introducing the presented additional new measurement line of rapid diagnostics before deployment, a hierarchical three-step diagnostics and assessment framework can be constructed. Considering the wide range of operating conditions, vehicles, and mission types, and also when faced with uncertainty or even a lack of data, a flexible tool must be applied that is a procedure rather than a simple formula, so that its parameters can be adjusted easily to the actual issue.

Test results are assumed to represent the actual and practical status of the batteries; however, there is no doubt that some uncertainty may occur, and that their accuracy is not absolute. In order to represent the uncertainty and the possible errors and deviations, the fuzzy methodology seems to be most appropriate. Using a multi-level rule method and introducing fuzzy signatures, the complex structure of data can be handled in a hierarchical manner. The fuzzy signature was first proposed by Koczy et al. [38] as a generalized form of vector-valued fuzzy sets, in the sense that it may have nested “sub-vectors” and sub-sub-vectors” for the vector components of the membership values. To summarize, a fuzzy set $A_f$ is defined as follows:

$$A_f=(X,{\mu }_A);{\mu }_A:X\to [0,1]$$

(1)

where ${\mu }_A$ is called the membership degree assigned to the elements of X. A vector-valued fuzzy set $A_{vvf}$ is the extension of the above:

$$A_{vvf}=(X,{\mu }_A);{\mu }_A:X\to {[0,1]}^k$$

(2)

where k is the number of the vectorial membership degree components. A further extension is the fuzzy signature (FSig), where:

$$A_{fsig}=(X,{\mu }_A);{\mu }_A:X\to \left[\begin{array}{c}{C}_1\\ C_2\\ \dots \\ C_k\end{array}\right],$$

(3)

where:

$C_i=\left\{\begin{array}{c}[0,1]\\ C_{ij}\end{array}\right.$, or where $C_{ij}$ is defined recursively, in the same manner.

Of course,$A_{fsig}$ can also be represented by a rooted tree graph, wherein the hierarchically nested sub-vectors are represented by sub-trees. The complete definition of the fuzzy signature, however, includes another important set of formulae: the full set of the fuzzy aggregation operations assigned to the intermediate (non-leaf) nodes, which may be considered as an “instruction to execute” for calculating the aggregated higher-level membership degrees. In the current case study, some novel aggregations based on engineering considerations will be proposed.

As FSigs are complex, hierarchical membership degrees, which are not entirely transparent; since, often, some components are missing, it is necessary to find a way to calculate simpler membership degrees by reducing the sub-trees to their respective roots, into a single membership degree assigned to the given (sub-)root. In order to calculate the reduced value, each intermediate node of the tree graph (or each membership sub-vector) is assigned a fuzzy aggregation operator (a monotonic operator preserving the extremal values 0 and 1), the execution of which combines the membership degrees at the “leaves” into a single value in (0,1), which will be associated with the former root, now becoming a leaf of the reduced “tree” after the reduction. This way, recursively, the whole FSig can be reduced to a single membership grade (in the root of the whole tree), if necessary. Regarding the mathematical structure of FSigs, the manipulations with partly different FSigs, and operations on the same FSigs, see [39].

The modeling method outlined above can properly represent uncertainty in the perception or definition of a non-deterministic nature, while it is suitable for reducing complexity by applying the aggregation operations and thus aggregating the available information into more compact models, even going as far as compressing them into a single fuzzy membership degree for a given element. In our case, the status of a battery is expressed as a percentage, or in another approach, the membership grade of suitability cannot be and is not given as a single, direct value, but must be calculated from a set of quantitative parameters forming the components of nested vectors (see, e.g., Figure 1). In the tree graph, the lowest-level elements are the leaves, whereas the ones on the levels between the root and the leaves are the intermediate nodes, which are connected by the branches (edges). Leaves form (often more closely connected) sub-groups of information, related to the higher-level roots of the sub-trees. The information contained in the combination of these leaf-assigned membership degrees may be calculated by the fuzzy aggregation operators in the intermediate nodes (the sub-roots of the respective sub-trees).

Figure 1 shows the battery system risk assessment scheme modeled by the fuzzy signature approach, here briefly summarized.

In Figure 1, X₁ stores the battery values from continuous use and the factors influencing the service life of batteries; these values are very diverse and can be examined using several approaches. Data collection in this case means continuous backup of data from use. Conditions recommended for such exemption by supplementing the temperature data of the different load profiles (current and voltage). The initial data stored in this way can be a great help when starting after longer storage. These values are very diverse and can be examined from several approaches, thus the current work does not cover this.

X₂ represents the values from continuous maintenance, wherein we take into consideration the two most important parameters, SOH and SOC. This is greatly influenced by the timing of the last test:

$$X_2=\left[1-\frac{t}{T}\right]\left(min\left(X_{21}{X}_{22}\right)\right)$$

(4)

where t is the period of time since the last maintenance and T is the time of expected maintenance. Equation (4) is the expression of a special parametric fuzzy aggregation operation. The min operation is the most classic t-norm that has already been used by Zadeh in the initial publications on fuzzy sets, and it expresses the strict condition that it is always the worse or stricter of the two components, SOH and SOC, that will essentially determine the sub-root degree. The parametric time-dependent factor $1-\frac{t}{T}$ influences the result, in the sense of a further decrease when the time that has elapsed since the last maintenance scheduled may negatively influence the reliability of the battery—based on a simple assumption of the essentially linear time-dependence of the deterioration procedure. The descriptions of X₂₁ and X₂₂ are given by the following equations (see Equations (5) and (6)):

$$X_{21}=\left\{\begin{array}{c}\frac{SOH \left[\%\right]}{100} if SOH=100\% then 1\\ \frac{SOH \left[\%\right]}{100} if 100\% \le SOH\le 90\% then 0.9\\ \frac{SOH \left[\%\right]}{100} if 90\% \le SOH\le 80\% then 0.8\\ \frac{SOH \left[\%\right]}{100} if 80\% \le SOH\le 60\% then 0.5\\ \frac{SOH \left[\%\right]}{100} if SOH\le 60\% then 0\end{array}\right.$$

(5)

The equations give the battery SOH, based on the X₂₁ output. Batteries below 60% are not recommended for use in this case, but even those in an 80% condition are only used in emergencies.

$$X_{22}=\frac{SOC \left[\%\right]}{100}$$

(6)

Using the equations, the output of X₂₂ can be determined from the initial value of the charge level. Based on the correlation, a higher charge level is associated with a lower risk.

Figure 2 gives an example of the relationship between the expected and the calibration performed.

The horizontal axis in Figure 2 shows the elapsed time since the last calibration. The vertical value specifies the value of the elapsed time multiplier. The possible states obtained after evaluating the result of the X₃ rapid test are as follows.

The aggregation merging the results of the measurements is proposed as:

$$X_3=min\left(X_{31},X_{32},\dots ,X_{3n}\right)$$

(7)

This simple t-norm-type Equation (7) aggregation expresses the statement that the cell in the weakest condition (lowest voltage) will determine the reliability of the whole system. It is possible to extend this model to a modular approach wherein the aggregation may consist of several sub-aggregations, combined by some monotonic operation. In this investigation, this extension was not applied.

Based on Figure 3, the larger the cell voltage deviation, the worse the condition of the battery. The percentage of deviation that is determined depends largely on the type and design of the battery (the value shown in Figure 3 is a guideline). The usability of the complete system is recommended, according to the following formula:

$$X=min\left(X_3,\frac{X_1+X_2}{2} \right).$$

(8)

This is again the formula of a novel aggregation, Equation (8), which was determined on the basis of engineering considerations. The arithmetic mean is a typical aggregation between the t-norm and t-co-norm range, while min is a t-norm (as mentioned above). The combination of the two is, however, a special operation that still satisfies the axiomatic conditions for fuzzy aggregations (preserving 0 and 1, as well as monotonicity). After evaluating the results, the following categorization can be determined (Figure 4).

Table 2. The possible categories, based on the test results.

	X1	X2	X3	X
I	0.9	0.9	0.9	0.900	A
	0.9	0.9	0.6	0.600	D
	0.9	0.9	0.3	0.300	E
II	0.75	0.8	0.9	0.775	C
	0.75	0.8	0.6	0.600	D
	0.75	0.8	0.3	0.300	E
III	0.6	0.7	0.9	0.650	D
	0.6	0.7	0.6	0.600	D
	0.6	0.7	0.3	0.300	E

shows a calculation example of the possible categories.

In Table 2, three possible situations are compared. In Case I, the batteries’ periodic maintenance (X₂) gave good results; the operational conditions (X₁) have also been favorable. In Case II, both X₁ and X₂ are considered as being at a medium level, while in Case III, the historical parameters X₁ and X₂ represent relatively poor levels. As is shown by the various rapid test results (0.9 = good, 0.6 = medium, 0.3 = poor), the final assessment results from the calculations obtained by executing the chosen aggregations within the fuzzy signature framework are different (see the last column of Table 2).

One of the difficulties of the method is that some phases require long measurements (Phase 2), while the other difficulty is that a great deal of data (Phase 1) is required for accurate estimation. Thus, the process is strongly affected by the amount of available data. A further difficulty may be the rapid test itself (Phase 3), as this is a pre-departure test, and this test may not be performed with sufficient thoroughness in a critical situation. The main limitation of the concept plan is that it contains many type-dependent factors; in addition, a specialized measuring system is required for the test. Furthermore, knowledge of the battery system that is being tested, along with well-trained personnel, are prerequisites for the applicability of this method.

5. Fast Cell-Health Assessment, Localization, and Classification

An electric vehicle was used for a fast-test demonstration. The applicability of the method was tested under real measurement conditions. A Nissan Leaf vehicle was used for the measurements and a Panasonic Toughbook CF-D1 was used to read the battery data. During the tests, the data were extracted by connecting to a vehicle diagnostics connector and were saved using the CONSULT III Plus program. During the test, 600 s of data was recorded, and the results are shown in Figure 5.

During the test, the operation of the cells and their deviations from each other were examined at higher speeds. Several accelerations and decelerations can be observed; the speed range was from 0 to 140 km/h. The cell voltage-range change is relatively large: from 4.1 V to 3.5 V. However, the values moved together relatively uniformly. To detect larger differences, we examined the voltage variances between the minimum and maximum voltage and the current load.

Figure 6 shows that the difference is not significant; however, at the moment of high load (270 A) between the smallest and largest cell, it can be up to 250 mV. This value is already a visible difference and can become an error if it occurs frequently. To filter out the weaker batteries, we examined which cell number in the system was the worst.

Table 3. Percentage distribution of the lowest-voltage cells, based on the serial number.

Cell number (ID)	0–5	5–10	10–20	20–30	30–40	40–50	50–60	60–70	70–80	80–90	90–96
Lowest cell voltage (%)	10.00	2.50	2.17	13.33	0.17	1.17	6.50	18.83	3.00	30.00	12.33

summarizes the location of the weakest cell in terms of percentage.

The first row of the table shows the cell number, while the second row shows the percentage of the cell that was the weakest during the test. In most cases, the cell with a sequence number between 80 and 90 has the lowest voltage, at 30%. Among the 600 s values, all batteries showed below-average voltage levels for some time, which means that there was no outstandingly good cell in the system. Since we only considered the worst case at that moment, the next step was to examine in how many cases a particular cell was worse than the average voltage level. Data analysis can also be used to determine which cells were at a voltage level of 80% lower than the average level, over the entire measurement range. For simplicity, the following table shows the index of only those cells that showed a below-average voltage for 480 s or longer for the entire duration of measurement.

The first row of

Table 4. Indexes of cells with below-average voltage.

Cell number (ID)	3	7	25	26	42	54	65	66	85	86	87	93	94	95
Time (s)	489	528	500	524	496	570	534	512	496	521	559	557	510	537

shows the cell serial number. The second row indicates the time in which the cell is below the average voltage. In some cases, the batteries are below the average voltage for more than 500 s. This definition does not necessarily mean that the cell is in a bad condition or needs to be replaced, just that these cells are most likely to fail. Another important factor is how many tenths of the cell voltage permanently deviate from the average. If a cell constantly deviates very slightly by a few 0.01 V from the average, this type of analysis can also classify this cell as being worse. Therefore, in the next step, we examined for how many seconds each cell deviated from the mean by at least 12 mV during the test (12 mv is 1% of the total measuring range).

Table 5. The deviation of 12 mV from the average.

Cell number (ID)	1	2	86	92	93	94
Time (s)	29	40	25	25	35	26

shows only those values where this was the case for nearly 5% (30 s) of the total measurement time.

The first row of Table 5 shows the cell serial number. The second row indicates the time spent in the critical range. Longer-term discrepancies typically appeared in the first and last elements of the system. The last step is to highlight the worst-performing cells and examine them separately. Based on the previous results, Cell Voltage 2, Cell Voltage 54 Cell Voltage 86, and Cell Voltage 93 were also tested separately, relative to the average voltage.

Figure 7 and Figure 8 show the average voltage line with a green horizontal bar (0 mv) and the 12-mV deviation with a red bar. The deviation of each cell is mostly below the green line but above the red one. This means that the batteries are operating at a below-average voltage, but not to a critical degree. Larger oscillations, or spikes, are visible at the moment of acceleration. Further measurements are needed to assess this criticality, but based on frequency and recovery, the cells are still in good condition.

To summarize the measurement and analysis results, we examined how many seconds the power deviated from the average voltage by 12 mV. Based on the results, it was found that even the weakest cells deviated to an acceptable extent, but the test method fulfills its purpose well. A further advantage is that the 1% deviation from the average voltage and the critical time can be further refined, depending on the application.

It is important to note that the method presented in this article was performed by measuring the battery system of a fully electric vehicle. However, the load profile of batteries used in hybrid vehicles is different. Our choice is justified by the fact that in the case of military vehicles, the full EV mode also occurs in a particularly critical situation, wherein it is not possible to operate the vehicle in the HEV mode. Furthermore, in such cases, it is important that the vehicle is continuously operational in a well-defined manner. The usability of the method for road HEV requires further measurements to examine the effect of switching between the two modes on batteries.

To verify the method’s accuracy, three measurements were performed on the battery systems. The test was performed on the same vehicle, with the same diagnostic tool and route. However, it is important to note that these are real vehicle tests, so the traffic situations were not always the same. In our analysis of the differences in the first cases, we found that it was important to examine the vehicle in the case of very frequent, less frequent, and minimal urban traffic. Thus, a total of 96 battery values were compared and analyzed in all three cases. During sampling, data were collected every second for 10 min in each case, so a large amount of similar and independent data was also recorded. For this analysis, a seconds-based evaluation was used, and each cell was examined separately at each time point.

During the test, we also analyzed for how many seconds the observed cell was under the average voltage, with a difference of 12 mV. For better observability, the test cell numbers were expanded, and all three measurements are shown in

Table 6. The deviations of 12 mV from the average, during the three measurements.

Cell number (ID)	1	2	7	20	54	65	86	87	92	93	94
Time_1 (s)	29	40	13	25	17	6	25	17	25	35	26
Time_2 (s)	18	33	10	26	20	6	26	17	29	32	21
Time_3 (s)	15	35	15	27	23	10	16	14	24	30	21

.

The time values in the first column of Table 6 indicate the different measurements: Time_1—minimum traffic, Time_2—medium traffic, Time_3—very frequent traffic. It can be seen that there are differences between the individual measurements, but the change is of a similar order of magnitude in each case. The differences are probably due to the different traffic situations. Measurements will also be performed on a proving ground to minimize the load on the battery system between measurements.

6. Discussion

Using the hierarchical assessment system formalized by the fuzzy signature graph structure and the aggregation operations assigned to the intermediate nodes, as described in Section 4, the actual risk and non-probabilistic type of uncertainty can be taken into consideration before military deployment. In order to reflect engineering considerations in the measurement and assessment procedures, a series of novel fuzzy aggregations were proposed; among these is one that is parametric, therefore allowing time-dependence when entering the final evaluation result. The aggregated result of the X Equation (8) is calculated by evaluating all membership degrees at the leaves of the tree, obtained from the measurements and observations; applying and executing all fuzzy aggregation operations that are assigned to the intermediate graph nodes gives a very informative single-parameter value, presenting a fuzzy membership degree within the unit interval, where 1 represents the absolute reliability and deployability of a battery, while 0 stands for a totally broken-down battery. All other degrees expressed the (estimated) partial reliability and expected performance of the power-supplying battery on hand. The final decision is based on threshold values that may be fine-tuned; thus, the acceptance limits can be modified, depending on the willingness to take risks and on other conditions, e.g., the state of combat, the type of the mission, including the geographic conditions, the roughness of the terrain, the availability of spare parts and components, and the access to service support, etc.

The model, based on the FSigs, may also be useful for simulating possible future situations in the short or the long term. By predicting the possible inputs and considering the time scale of the military operation, the expected risk can be evaluated at a fleet level as well by merging the information obtained from the fuzzy signatures that describe the condition of all batteries within the fleet of vehicles, e.g., by applying a simple aggregation of all root-reduced degrees, such as the min or the arithmetic mean. This may be especially useful when a long time scale does not allow for periodic battery maintenance and inspection to be performed within the scheduled time. In that case, X₂ can be formally “negative”, which is represented in the fuzzy membership degree range by a 0, or it may involve some more complicated fuzzy operations; however, these will not be discussed in this study, as they need some serious algebraic considerations, and the assumption of certain mathematical conditions—in any case, the final value of X is very likely to be rather low, resulting in the rejection of the given battery (see Equation (4)).

We claim that our novel model and evaluation protocol proposed in this study gives tactical support for the maintenance process, highlighting the main sources of risk. In combat service, resources are limited, and there is usually a strong time pressure as well. A poor membership degree value of X₃—obtained from the result of the rapid on-the-spot test—will rule out the deployment of the batteries in the mission. However, fixing/replacing some of the tested and lowest-performing cells can improve the value obtained in X₃ significantly, so that the unit can pass the acceptance limits.

In the current phase of this work, the method has been developed and examined using several measurements. As work continues, we will perform additional measurements using systems with poor battery conditions and other types of fully electric vehicles (further examining the X₃ in this article). In this case, several different battery systems are added to the database and are given a unique ID. This creates a complex measurement database and structure. The next step will be to test the system during maintenance, to refine the built-in estimators (for more information on X₂). The third phase of the research will be focused on the detailed parametric representation of historical operating conditions and circumstances. The actual and quantified relationships between the operation and/or storage history (total operation time, cycles, charging, external temperature, etc.) of the cells and the possible compliance with theoretical technical specifications need to be investigated in laboratories and in the field as well (X₁).

Due to the constantly expanding database and the various data, the initial fuzzy graph will be modified and expanded upon later. Aggregation processes are additionally weighted after a better understanding of the critical degradation factors.

Another important area to be examined will be the analysis of the duration and impact of the rapid test. A fuzzy learning algorithm that can determine the measurement steps independently, based on the condition and type of the battery system, can be particularly useful in this analysis.