Systems of Systems Approach to Modeling Lunar Bases

Jason Held∗, Juergen Schlutz, and Britta Ganzer†∗Saber Astronautics, Denver, CO

†Institute of Space Systems (IRS), University of Stuttgart, Germany

This paper presents a Systems of Systems (SoS) approach to measuring lunar base performance. Theability to measure a lunar base using an appropriate set of metrics and attributes allows designers to choosequantitatively between different options. The method is to use a high level systems analysis to determineappropriate functional attributes and metrics, then to learn their interactions using probabilistic graph models.The interaction model is used to determine a score for each design option by estimating performance of thegroup. Results demonstrate how lunar base scenarios are quantifiable in a data driven fashion.

I. Introduction

When faced with the design of a human occupied lunar base, engineers are confronted with a wide variety ofoptions, requirements, and constraints, which together are used to select systems for the lunar base. Major optionsin the design include the location of the base, number, size and functionality of base modules, and their distributionand configuration together with a preliminary operations plan for astronauts, vehicles, robots, and other elements toevaluate the base performance with regard to mission objectives.

A first approach to numerically support lunar base design was implemented in the LUBSIM (lunar base simulation)tool by H.-H. Koelle in Berlin, which simulates construction and operation of a lunar base.1 Primarily concerned withmass flow, masses and distributions are quantified in order to derive values for cost and utilization potential of a lunarbase. This implementation however does not allow optimization of the system and only facilitates calculation, whileall design decisions - be they right or wrong - are totally dependent on the ability of the system engineer.

Another approach to evaluating designs is Equivalent System Mass (ESM), which can be calculated on systemand subsystem levels. It comprises installed system mass as well as the required mass flow over mission time.2–4 Onsubsystem level the mass effects on other subsystems are also accounted. In the case of the Environmental Controland Life Support System (ECLSS), different power needs or thermal loads may evolve from different designs. Thisleads also to different power and thermal masses. Compiling the total launch mass of the mission, the ESM provides aquantitative comparison of system costs. However, it does not provide a quantification of system performance, failuretolerance, redundancies, safety and reliability issues. Here, like in LUBSIM, assessments are mostly qualitative.

The key question is: how is performance for lunar bases defined and measured? There are many moving parts(human, robots, etc.) and complicated environmental variables (radiation effects, space weather events, mission pa-rameters, etc.) affecting solution. Placement of objects (such as habitat structure and fuel depot) can also causeperformances to change as drastically as a change in mission. Factors such as ECLSS, thermal, object placement, hu-man action, and the environment, are all interrelated. Functions for performance are complex, emergent, and difficultto predict a priori. This results in many design options which can satisfy the problem constraints but cannot be com-pared. Qualitative methods can find valid options but cannot choose even a locally optimal design for implementationbecause the interactions between variables are not closely considered.

This paper presents a “Systems of Systems” (SoS) approach to measuring lunar base performance, as a prerequisiteto high level design. Measuring an SoS has the challenge of verifiability to ensure that measurements are solving theintended performance modeling problem. Here it is not enough to ask how to observe data as much as it is to knowwhat to observe in the first place. Recent advancements in SoS Engineering (SoSE) show specifically how to findreasonable and complete metrics for an SoS problem, then show how the SoS can be modeled using the learnedinteraction of metrics and functional attributes called a System Map.5–7

∗Jason Held, Saber Astronautics, Denver Colorado, Member AIAA, jheld@saberastro.com.†Institute of Space Systems (IRS), University of Stuttgart, Germany, schlutz/ganzer@irs.uni-stuttgart.de

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The first step is to find a “complete” mapping of metrics and functional attributes (properties) the desired systempossesses. Measurable environmental variables will be compared in the same model as base behaviors and subsystem(such as ECLSS) performances. A simulation is conducted for a variety of combinations of valid objects in the lunarbase’s inventory, recording metrics of the SoS state over a discrete set of time. The next step is to find parameters formetric and functional attribute interactions using statistical learning tools which can handle dynamics, emergence, andswitching characteristics.

A Dynamic Bayesian Network (DBN) is used to learn relationship between metrics and functional attributes.DBNs relate variables to each other over adjacent time steps and are successful in determining highly complex, non-linear interactions with emergent properties and missing data.8, 11 It has shown to produce equivalent solutions toHidden Markov Models and Kalmann Filters.11 This makes them suitable to learning models for SoS in a complexenvironment but only if the lunar base remains in the same mode of operations. Switching states in a DBN (a.k.a.,change in mode) such as occurring during a space weather event, would require a separate model or “hidden nodes”,which are computationally expensive and require domain knowledge. A separate operations configuration, such asduring astronaut “down time”, also requires a separate DBN. Gaussian Mixture Models (GMMs) are widely used inthe computer vision recognition to discretely identify objects in an image.17, 18 GMMs are used to identify statisticaldata mixtures corresponding to individual modes of operation, allowing the system to identify the “respond to spaceweather event” and “down time” DBN model. The identification of a space weather event by the GMM causes themodel to switch to the closest DBN model. With attributes monitoring subsystem performance and some monitoringthe interaction between the group and the environment, the complex relationship between the SoS players can bereasonably understood. The interactions in a System Map allows close coupling between mission and engineeringvariables, solving both problems in a data driven fashion using a single framework.

Preliminary results from simulations of a Lunar base at Shackleton Crater are presented which show how to findoptimal number of mission modes, then demonstrate the accuracy of Systems Map in estimating Lunar base state.Results also demonstrate how functional attributes change based on environmental condition and subsystem degrada-tion. Mission mode switching is modeled and observed. Then a short comparison of different degraded subsystemconditions (ECLSS failures) is conducted to show how performance scores of a “mission critical” functional attributecan be used in high level analysis.

This paper is organized as follows. Section II overviews the SoS modelling method. Section III uses the methodto derive metrics and functional attributes for a Lunar Base problem. Section IV describes the simulators. Section Vdiscusses the results. Section VI concludes and discusses the direction of future research.

II. System Map: The SoS Modelling Approach

This section is a brief overview of the SoS modelling process.5 A System Map is a set of probabilistic graphsmodeling both continuous and discrete interactions between system level metrics and Functional Attributes (FAs).Each graph represents a single mode of Lunar base operation, for example, a communications satellite transmittingduring a geomagnetic storm will have different performance functions than transmitting during normal space weatheroperations. Fig. 1 shows an example of a single System Map mode. In the graph each node represents a data drivenmetric, describing system level performance, as measured on spacecraft subsystems and components. Arrows representknown (or learned) causal dependencies. Metrics interact with each other (not shown for simplicity) and feed into FAswhich are quantitative descriptors of mission performance. A probabilistic learning function quantifies interactions foruse in the model.

This SoS modelling was used to accurately model the performance of multiple Unmanned Aerial Vehicle (UAV)teams tracking randomly moving high speed targets.5 The research showed System Maps constructed offline to beversatile and accurate enough to handle real time implementation of new dynamics without relearning the model. TheUAV study was the first data driven SoSE study, showing a direct path from high level qualitative abstractions (such asmission goals) to lower level quantitative measurements (metrics). Since the approach proved accurate for scenariosof very high complexity and emergence it is a viable candidate for Lunar base SoS performance modeling.

The steps of an SoS process are: 1. Determine what to measure, 2. Determine how to measure, 3. Form the modelsfrom historical data, and 4. Implement the model on a spacecraft system.

A. Step 1: Determine What to Measure

SoS analysis is a top down process starting from mission and modeling goals and resulting in a complete set of metricsand Functional Attributes (FAs). It includes,

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Figure 1. A System Map models the interactions between metrics (small circles) and Functional Attributes (big circles). Arrows representa causal connection identified from statistics of metric and FA history. Metric interactions are not shown for simplicity. Mission criticalFAs (larger dark circles) form the scoring function measuring success of the System Map given its parents. This graph represents a singlemode of operation.5

• Mission, system definition, and modeling goals. This encapsulates Lunar base mission, subsystem mission,and the modeling goals. It defines the boundary between system and environment the system operates in.

• High level attributes (HLA). These are high level properties any SoS may have. The task is to identify theones specific to Lunar base performance. HLAs are organized by the type of measurements that can occur,such as “operations” and “command” within the following abstract groupings: internodal (inter system inter-actions), extranodal (external factors affecting the system), and information (how information qualities affectsthe system). Note that HLAs are not quantified, simply used with mission specifications to guide development ofFunctional Attributes and metrics (below).

• Functional attributes (FA). Within each HLA are attributes which functionally describe the behavior of theSoS. Functional attributes are quantified by data driven metrics. The SoS engineer designs FAs based on HLAparent and mission/modeling goals.

• Metrics. Within each FA are metrics which are engineered, measured, and benchmarked during the data collec-tion task.

Fig. 2 shows the process of determining metrics and FAs. First the SoS engineer chooses HLAs based on missionand modeling goals. FAs are chosen within each HLA which are quantifiable by a set of metrics. The final task is toengineer metrics for use in measuring each FA. The result of this step is a complete set of metrics and FAs quantifyingthe SoS.

B. Step 2: Measure

Forming SoS level metrics and FAs requires the following actions:

1. Collect Data. Spacecraft typically store health and welfare telemetry. Including Lunar environment and otherinformation is possible with a few assumptions. Detection of Lunar environment conditions (radiation andcharge) lie outside the scope of this paper, however several detection methods exist or are under active re-search.9, 10 Collection and dissemination of data is centralized to an onboard base computer, in this case, thesimulation computer.

2. Calculate Individual Metrics. The computer calculates metrics for each individual node using the currenttimestep’s collected telemetry.

3. Calculate System Level Metrics. The computer calculates system level metrics, hereon called SoS metrics.SoS level metrics are the composite of individual metrics, usually (but not exclusively) defined from the averageindividual performance scores.

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Figure 2. Top Down analysis starts with mission and modeling goals and ends with metrics to be measured. Note that quantifiabilityincreases as you get closer to metrics. The purpose of HLAs and higher abstract groupings is simply to guide the process of determiningwhich Functional Attributes and metrics reasonably define the problem based on mission and modeling goals.5

Functional Attributes will be calculated directly from their metrics as defined in Step 1.

1. Metric calculation. Each metric is defined during SoS analysis. A function for each is constructed based onthe definition, then benchmarked on the definition’s theoretical maximum. If no theoretical maximum exists,the maximum observed will be used. The metric function can consist of several measurements taken either fromone or more telemetry items.

2. Functional Attribute (FA) calculation. Calculation of each FA occurs by finding the weighted mean of itsassigned metrics’ Maximum Likelihood Estimates (MLE).13, 16 The weight, b, is constructed from rank orderingeach metric based on its importance to the FA. Importance is based on two factors:

(a) Variance. Metrics with less certainty have less impact on the FA. It is scored from metric i’s variance attime t,

vi = 1 − σ(t)i . (1)

(b) Density/agreement. Metrics closer to a density cluster are considered more important because the clus-tering represents agreement (clarity) in behavior of the attribute. Clustering represents commonality ofmetric behavior. Metrics are scored from the distance to the common, where the cluster is understood asthe mean of the metric MLEs. The distance is given as,

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cdist = 1 − |M (t)i − θ̂|, (2)

for each metric Mi at time t and θ̂i is the MLE for metric i.

The FA score is calculated from each metric Mi (of n metrics in the FA) as,

FAscore = αn∑

i=1

bi(θ̂(Mi)) (3)

where α is the normalizing constant and the regression weight bi is the ranked product of the scores,

bi =cdistvi

arg max(cdistvi). (4)

The end of this step will result in the ability to calculate metrics and FAs at every timestep.

C. Step 3: Form Model

Forming the model occurs by finding parameters for metric and FA interactions using probabilistic learning toolswhich can handle dynamics, emergence, and switching characteristics in a non-linear state space model.

A composite of Dynamic Bayesian Network (DBN) and Gaussian Mixture Models (GMM) learn the relationshipsin a System Map. DBNs relate variables to each other over adjacent time steps. This makes them suitable to learningmodels for SoS in a complex environment but only if the Lunar base remains in the same mode of operations, suchas “astronaut on EVA”. A single mode is represented by a single DBN model. Switching states in a DBN (a.k.a.,change in mode) such as occurring during a space weather event, requires “hidden nodes”, which are computationallyexpensive and require domain knowledge.

A Lunar base “mode” means a multidimensional dataset describing a statistically grouped behavior pattern, iden-tified by distance to a mixture in the GMM. Mode changes can occur due to spacecraft controller action, such ascommanding the spacecraft to enter a “safe” software state. A change may also occur due to spacecraft autonomy,such as the act of maneuvering, or taking a photo at a specified time. Actions outside the influence of spacecraft orcontroller, such as during a space weather event or space control event, are also identifiable as a mixture in the GMM.Switching may also occur due to a complex, emergent dynamic. The GMM can identify all of these conditions asmixtures, while the DBN accurately models the chosen individual condition.

The solution in this paper uses Gaussian Mixture Models (GMM) to discretize each switching state. GMMsare used to identify statistical data mixtures corresponding to individual modes of operation, allowing the system toseparate the “respond to space weather event” and “conserve EPS power” DBN models. The combination also hasthe potential to statistically identify failure modes and anomalies. With attributes monitoring subsystem performanceand some monitoring the interaction between the group and the environment, the SoS interactions can be reasonablyunderstood. The interactions in a System Map allows close coupling between mission and engineering variables,solving both problems in a data driven fashion using a single framework.

There are two important considerations with this approach.

1. Modes are unspecified. Mixtures in the GMM are treated independently, so there is no explicit specificationof modes to mixtures. This is both an advantage and a disadvantage, as specific modes of interest (such ascommunicating during a geomagnetic storm) will not be stated but will have identifiable characteristics in thedata. The mixtures are abstract and can be autonomously identified provided the correct metrics were chosenduring SoS Analysis step.

2. Tuning. Finding the optimal number of mixtures is a common requirement for GMM. Too few mixtures willresult in a loss of accuracy in the model as certain modes will not be represented. Too many mixtures mayresult in overfitting. A locally optimal number is determined by adding and removing mixtures from the trainingdataset until reaching greatest accuracy.

Identification of mode in real time is a distance function between current SoS state and the average of each GMMmixture. Once the closest mixture is identified from the training data, DBN learning is conducted to form a modelbetween all metrics and FAs within the mixture. Each mixture has its own DBN, constructed offline and stored on thespacecraft computer.

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D. Step 4: Implement Model

The process consists of using the previously learned System Maps in online estimation. The runtime process is asfollows,

• Start a simulation.

• Calculate the metric and FA scores at each current time step.

• Estimate the current GMM mode in each Lunar base configuration’s System Map using the distance function,estimate the next timestep’s metric and FA performance using the following linearization function Eqn. 5. Theestimation of each metric is based on parenting order and weight, b, learned in the DBN. This prediction is basedon the local conditional density function for each metric (or FA) Mi,

P (Mi|PA(Mi)) = N(Mi;µi +∑

Mj∈PAi

bij(mj − µj);σi), (5)

where PA(Mi) is the causal parent of Mi, mj and µj are the values and means for each parent, bij is the weightbetween metric i and j, and σi is the variance.

The experiments will demonstrate the feasibility of the approach for the Lunar base problem by estimating metricsand FAs, then scoring the distance between estimates and values using Kullback-Leibler (KL) divergence.14

III. SoS Analysis - Finding the Right Metrics

This section is an implementation of the SoS paradigm described in Section II. It starts with a brief definition ofthe SoS, discusses it’s nodes in a top-down fashion, and results in the FAs and metrics used for experimentation.

A. SoS Definition and Mission

The primary purpose of the base is to maintain a healthy environment for human occupation. All designs must supporta crew of four astronauts for one year, with a logistics resupply time planned every six months. The goal of the modelis to quantify the feasibility of base operations, which for this preliminary study refers to survivability of the crew andequipment.

The scenario places a Lunar Polar Base at Shackleton Crater Rim. The nodes in the base interact using either massflow, electric power, or telemetry communications as in Fig. 3.

Figure 3. A concept sketch of interactions within a Lunar base. Mass, electric power conditions, and telemetry all may affect the nodes inthe SoS.

1. Nodes

The SoS consists of the several types of nodes. The types of nodes, combinations and quantities are left to the SoSdesigner to determine. Nodes may be placed at certain times and combinations to suit the missions. Their definitionsare:

• Habitat Module.

• EPS Modules.

• Laboratory.

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• Greenhouse.

The Habitat, Laboratory, and Greenhouse modules are pressurized. Solar and fuel cells produce power from eachEPS module.

2. Environment

The environment consists of anything which can influence the SoS. Since the SoS is scoped to the moon base itself,the environment is the lunar surface and logistics resupply. Therefore, the following factors are considered importantfor the environment:

• Radiation. Lunar surface radiation conditions occur due to constant and periodic solar conditions. Radiation isa hazard for both crew and materials.

• Solar cycles. Periodic solar conditions will affect the SoS.

• Surface temperatures. Lunar surface conditions will affect SoS operational thermal requirements as well ascommon “wear and tear” maintenance rates.

• Lunar dust. Lunar dust was observed to be paramagnetic, highly abrasive, and difficult to clean. This will affectSoS maintenance and operations requirements.

• Meteorite Impacts. Impacts may cause damage and disrupt base operations.

• Logistics Resupply. A periodic resupply is conducted based on predictions from Earth groundstations, whichare scoped outside of the SoS.

For simplicity in this first study, meteorite impacts and lunar dust were not simulated.

B. High Level Attributes

The High Level Attributes (HLA) are examined based on mission and SoS definitions. Valid HLAs remain as thedomain for development of FAs and metrics.

1. Internodal Interactions

• Operations. Many nodes have decision making processes of various different types. The missions themselvesalso have operations which will need to be tracked with functional attributes. This is an attribute of the SoS.

• Command. Command structure may change depending on mission conditions. It may also change due to actionsof the nodes themselves, making command a valid HLA.

• Communications. Nodes communications may affect performance on the mission and are therefore a validHLA.

2. Extranodal Interactions

• Active. The SoS definition is scoped only towards the lunar base, in order to keep the problem focused to factorsand SoS designer can influence. However this leaves external factors which can still affect the SoS. Logisticsresupply is one external factor which can drastically affect the SoS but also directly responds to the SoS’ state.Active HLA is included in the metric space.

• Passive. Many factors such as solar radiation or thermal effects will change SoS performance but does notrespond to the SoS itself. Passive extranodal interactions are included in the metric space.

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3. Information

• Perception. Attributes of perception include logistics functions as well as the SoS’s view of its current state.

• Memory. Information stored about the physical environment and nodal displacement are part of the memoryHLA, as sensing is not consistent across the nodes.

All HLAs exist in this highly heterogeneous and complex SoS, the fullest metric space is deemed necessary todescribe the SoS. The next step is to examine SoS modelling goals, to determine which HLAs can be removed for thespecified modelling problem.

Examining model goals show that Memory HLA is not needed, since the mission is simply survivability of astro-nauts and equipment. If the mission was changed to surviving and exploring, the Memory HLA will return because ofthe need to track individual astronaut sensors and actions. Therefore Memory HLA is removed for this study. Activeattributes are also not needed since for this initial study logistics resupply is locked to 180 days. Allowing the Earthground station to change this based on telemetry (or base requests), would reactivate this HLA and all of its FAs andmetrics. Finally, although command and communications are important parts of the Lunar Base SoS, they are removedin order to allow a simpler validation of the method in this initial study.

C. Functional Attributes

Each HLA is examined using model goals and SoS definitions to determine appropriate Functional Attributes (FA).

1. Operations.

• Disposition. Physical disposition quantifies the physical layout of the lunar base. It is unlikely to change duringthe course of a simulation so is included here for posterior analysis. Disposition is quantified by metric Centrality

– M11: Centrality. All nodes were positioned within the operative range of the lunar base. Their distributionsignificantly impact base operations. Modules and elements are grouped close together for easy accessand links, while maximizing excursion range for robots and humans. Each node’s position is quantifiedby coordinates in a virtual lunar base coordinate system and the distance to the virtual center of the base(usually placed in the habitat element). It is normalized by the maximum distance of the base elements,RGmax.

M11 =1n

n∑i=1

√x2

i + y2i

RGmax, (6)

where xi and yi are the x and y positions of node i (of n nodes). This metric is static for a specific lunarbase but is used to assess different configuration layouts.

• Personal Survivability. Quantifying the ability for astronauts to survive is a functional attribute measuringphysical human limitations during the mission. This is measured as a function of astronaut hunger, workload,rest and breathability of the air.

– M3a: Hunger. A relationship between consumption and workload was identified in previous work, eventhough they are separately measured.15 Hunger is a function of food available, f , with the added as-sumption that the crew will conduct rationing based on remaining food, ft, at time t over the time until alogistics resupply, tr. Hunger is estimated for the entire crew and not simulated on the individual level.Each astronaut requires 0.56 kg of dry food per day. The metric is astronaut consumption benchmarked bythe required consumption plus 10%, which is taken as a maximum reasonable consumption. For the sakeof simplicity, feasting was not simulated in this study.

M3 =ft

tr ∗ 1.1 ∗ 0.56 ∗ a, (7)

where a is the total number of astronauts in the crew. If ft reaches beneath the threshold of 7 days and theresupply time tr is greater than 7 days, a state of starvation is reached, Mhunger = 0.

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– M3b: Thirst. Similar to Hunger, thirst is measured based on rationing the remaining drinking water, wt.Each astronaut requires 2.8kg of potable water per day. If wt falls beneath a threshold of 7 days and thetime until resupply, tr, is more than 7 days, death of thirst occurs. If this happens, M3b = 0.

M3b =wt

tr ∗ 1.1 ∗ 2.8 ∗ a. (8)

– M6b: Breathability. There are two critical factors for breathability. The first is the volume percentage ofoxygen in the atmosphere, the second the volume percentage of carbon dioxide. The quality of breathableair in benchmarked as a distance from perfectly breathable air. Perfectly breathable air is defined by O2

volume percentage of 21% (CO2,opt) and CO2 volume percentage of 0% (CCO2,opt). These numbers arevalid for normal atmosphere pressure of 1.013bar, which is maintained by adjusting the nitrogen volumepercentage.M6a, benchmarks the O2 volume percentage, CO2 . The tolerable range of the O2 volume percentageat normal pressure is from 8 − 50%, where CO2,min states the minimum of 8% and CO2,max uses themaximum of 50%.

M6a =CO2,max − CO2

CO2,max − CO2,opt, (9)

for CO2 > CO2,opt or

M6a =CO2,min − CO2

CO2,min − CO2,opt, (10)

for CO2 < CO2,opt

– M6b: Breathability. This benchmarks the CO2 volume percentage, CCO2 . A CO2 percentage above 1%is considered toxic, which is assumed as the maximum tolerable level, CCO2,max.

M6b =CCO2,max − CCO2

CCO2,max − CCO2,opt, (11)

• Equipment Survivability. Equipment, to include habitat, rovers, and all subsystems measure survivability basedon metrics relating to wear. Wear and tear rates for structural components are affected by thermal, vibration,and stress loading. This functional attribute quantifies the ability for equipment to perform its assigned missionbased on its current maintenance state. Maintenance state generally degrades as a function time and use. A poormaintenance state will cause greater astronaut workload in the form of repair time.

– M7: Wear Electric. Wear and tear rates for electrical and solar components are derived from AIAAhistorical data. Wear is measured as electrical inefficiency, fi on each node i, which will increase overtime due to rust, outgassing, and solar radiation. The SoS level metric calculates the average inefficiencyover all components in the SoS, benchmarked by individual node manufactured electrical efficiency, fis

.

M7 =n∑

i=1

fi

fis

(12)

where n are the number of nodes in the SoS. The inefficiency fi is estimated as a degradation from thetime since the node received replacement parts, accelerated during space weather events.

2. Passive.

• Solar Flux. This FA describes the state of solar flux as measured by sensors on the base.

– M51: Solar Radiation.This metric describes the state of the solar flux at lunar surface level, which is de-pendent on time, surface location and topographic features. Due to the difficulty of simulating topographiceffects, Sun straight-line visibility is used to as a simulation driver.

M51 =1n

n∑i=1

Si

Smax, (13)

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where Si denotes the solar flux received at each node as an output of the simulation. It is zero if the nodeis in shadow and varies around the mean solar constant of 1368W/m2 when in sunlight. It is normalizedagainst a maximum expected solar flux at Moon distance, Smax, of about 1430W/m2.

– M51b: Solar Illumination. The illumination area for each module is also dependent on time, surfacelocation, and topographic features. Again, Sun straight-line visibility is used as a simulation driver.

M51b =1n

n∑i=1

Ai

Ai,max, (14)

where Ai is the illumination area for each node, which is zero when the node is in shadow. Ai,max isthe normalization factor, which is the surface area for modules, or the solar array surface area for powerelements.

• Useability of Terrain.

– M52: Terrain Roughness This measure the roughness of the terrain environment within exploration rangeof the lunar base. It is calculated from the maximum elevation difference in proximity to the base and doesnot change for a selected location.

M52 =hmax,RG − hmin,RG

Href, (15)

where hmax,RG and hmin,RG are maximum and minimum elevation in the exploration range RG (10km)of the base, respectively. Href is a reference maximum elevation difference and set to 5km.

• Radiation Difficulty. Radiation levels are measured at each time step. The functional attribute at a time step is astatistical understanding of overall difficulty of operating for the SoS at it’s current position at the given time.

The sun cycle is a measure for the radiation environment, i.e. the expected radiation exposure of the base forGalactic Cosmic radiation (GCR) as well as the probability of Solar Particle Events (SPE). It is characterizedby the radio flux at a wavelength of 10.7 cm. As the simplest assumptions, this flux varies periodically over thesolar cycle of 10.3 years (average), with the minimum of cycle 23 having been in May 1996:

F (t) = 1 − cos(2π

10.3a· (t − T23min)), (16)

where t is the time (Julian days) and T23min is the time of the correlated minimum, i.e. 1 May 1996.

– M53: GCR radiation levels. This metric describes the levels of GCR, which follows a contra-cyclic evolu-tion to the F10.7 radio flux, i.e. the intensity is high at solar minimum and low at solar maximum.

M53 = 1 − F (t), (17)

where F (t) is the maximum and minimum radiation level expected based on solar activity at time t.

3. Perception.

• Thermal State.

– M61: Heat Rejection Balance. The heat rejection balance of the base system is calculated from the in-dividual thermal control requirements of each node. It is indicated by the percentage of the full installedheat rejection capability of the base system that is needed at a given time, i.e. the required heat rejectionof each node Hi,rej divided by the total heat rejection capability Hbase,rej . To account for the limitedlifetime of the thermal control system (mainly due to the degradation and dust cover of radiating surfaces),the heat rejection capability decreases over time by a factor of dt (regular maintenance activities could beenvisioned to limit these impacts).

M61 =n∑

i=1

Hi,out

Hbase,out · dt/lat

, (18)

where the expression t/la is time divided by one year.

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– M62: Heating Requirements. This metric describes the required heating of the base system, calculatedfrom the individual thermal control requirements of each node. Heat requirements also has a direct impacton the power consumption of the base due to the (usually) electric heater system. It is indicated by thepercentage of the full installed power provision capability of the base system that is needed for the thermalcontrol system at a given time, i.e. the required heating of each node Hi,in divided by the total installedpower Pbase and the electric efficiency of the heater system. Degradation of the power system, especiallydue to the solar cell surface degradation, is also introduced through the factor dt.

M62 =n∑

i=1

Hi,in

Pbaseηheaters · dt/lat

. (19)

• EPS State.

– M63: Power provision. This metric describes the power consumption of the base system as a sum of thenodes’ individual power generation capabilities Pi, provided and as the percentage of the total installedprovision capability Pbase,installed. Power values already include any electrical storage and conversionlosses due to the power system hardware selection. Degradation of the power system, especially due to thesolar cell surface degradation, is also introduced through the factor dt and accounted for both in providedand installed power figures.

M63 =n∑

i=1

Pi,provided · dt/lai,t

Pbase,installed · dt/lat

=Pbase(t)

Pbase,installed(t). (20)

– M64: Power consumption. The power consumption of the base system is the sum of the nodes’ individualpower requirements Pi, in and as the percentage of the total installed power provision capability Pbase.Pbase already includes any electrical storage and conversion losses due to the power system hardwareselection. Degradation of the power system, especially due to the solar cell surface degradation, is alsointroduced through the factor dt.

M64 =n∑

i=1

Pi,in

Pbase · dt/lat

. (21)

• Consumable State. The crew perceives their consumable state by comparing the current stored mass mstored,t

at each time step to the initially stored mass mstored,0 after a resupply.

– M65: Consumption State. The crew perception of dry food and water mass.

M65 =mstored,t

mstored,0(22)

IV. Simulations

A. ELISSA Software Tool

The software tool ELISSA (environment for life support simulation and analysis) is used for ECLSS simulations.ELISSA was developed at the Institute of Space Systems at the Universitaet Stuttgart, based on the laboratory soft-ware LabView. ELISSA provides information about the cabin air composition, mass fluxes and losses at any givensimulation time. Furthermore, the power consumption and the heat rejection are observed. During simulation theparameters can be interactively adjusted.20 The time step of conducted simulations was set to 10 seconds and theobtained data were logged every 5, 000 simulation seconds.

1. Initial Simulation Inputs and Assumptions

For the moon base an advanced ECLSS concept was designed to support 4 astronauts for several years, with a resupplyinterval and a crew rotation of 180 days (time steps every 5000 seconds). It comprised physico chemical as well asbiological based technologies. The subsystems were chosen to form a flexible and regenerative system to minimize

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Figure 4. The Lunar Base Metric Space used in this mission modelling problem. Command, communications, memory, and active areall deactivated for the modelling problem, which is concerned only with survivability of the human crew. FA “Personal Survivability” isconsidered mission critical

resupply. The ECLSS regenerates oxygen, water as well as part of carbon in terms of in-situ food production. Table 1summarizes the components of the ECLSS and their tasks. An electrochemical depolarized CO2 concentrator (EDC)is used to filter carbon dioxide from the cabin air while a water electrolysis unit provides oxygen. These devices aresupplemented by the PBR. Wastewater including urine is treated by vapor phase catalytic ammonia removal system(VPCAR) to produce potable quality water. The VPCAR utilizes distillation, oxidation and reduction processes to filtercontaminates from the water, producing brine. An air evaporation system (AES) then extracts any remaining waterfrom the brine. The PBR and greenhouse as well as supplies from storage provide food. Solid waste is decomposed inthe solid waste incineration system (SWIS). The PBR handles a third of CO2, the rest is reduced in the sabatier reactor(SR) to methane. Most of the components do not stand alone; they interact with both the crew and each other.

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ECLSS SolutionsTask Technology

Atmosphere ManagementCO2-Removal EDCO2-Generation PBR

Electrolysis PBRTemperature and Humidity Control Condensing heat exchanger

CO2-Removal EDCWater Management

Waste Water Treatment VPCARBrine Treatment AESFinal Polishing MilliQ

Food ManagementStored food

PBRGreenhouse

Waste ManagementSolid Waste Treatment SWIS

CO2 Reduction SR

Major resupply items as summarized in Table 1 are nitrogen for atmosphere leakage compensation, water, food,and nutrients for plant and algae.

Resupply ItemsItem Resupply / 180d (kg)

Nitrogen 350Water 250Food 300

Nutrients for plants / algae 70

2. ECLSS simulation scenarios

Simulations were conducted for nominal operation and for various failures of the system. In nominal operation oneresupply interval of 180 days with a crew size of 4 persons was simulated. The process capacities of the all componentswere set in order to treat or generate the sufficient amount of material. The failure scenarios include single malfunctionsof critical subsystems:

• CO2 removal,

• O2 generation and

• Waste water treatment.

For single malfunctions, it was assumed that the subsystem is made operational by repair or backup once the criticalpoint for survival is reached. Therefore the entire time span of 180 days including system recovery was simulated.Further a total ECLSS breakdown and resupply shortage in water and food were simulated for the time span until thedeath of the crew occurred. With the loss of the crew system recovery is not considered.

B. Lunar Base Simulation

A simulation tool developed at the IRS was enhanced in order to analyze environmental impacts on the base withrespect to site location, the surface environment and influences from solar system bodies such as the Sun and Earth.

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This simulation is partially integrated into the 3D modelling tool Cinema 4D to generate the base configuration andmain parameters, and is coded in C++. Initial simulation place the lunar base on the lunar reference sphere of 1737.4km radius.

The simulation retrieves positions of the Moon, Sun and Earth from NASA’s solar system ephemeris files usingthe SPICE libraries.22 They are transformed to the Lunar base coordinate system using the surface location in order tocalculate relative positions and viewing angles and to determine visibility of the bodies from the base.

Using the 3D model and Microsoft’s Direct3D libraries, illuminated areas can be calculated for each lunar baseelement at any given time, allowing simple thermal budgets based on internal energy dissipation, radiative heat loadsand heat rejection capabilities of the module surfaces (Table B).

Inputs and Outputs of the simplified simulation model (all modules)Inputs Outputs

Surface location (lat, long, height) Illuminated surface areasSimulation start time Heat rejection/provision requirements

3D base modelThermal properties (absorption, emission, internal dissipation)

C. Initial Simulation Inputs and Assumptions

All metrics specified above can directly be derived from the simulation outputs in order to inform the Systems ofSystems model.

For the first iteration, the model of a potential lunar outpost for a permanent crew of four astronauts included asingle habitat, laboratory, and greenhouse. It also included two EPS modules (photovoltaics and fuel cells for storage).The outpost is assumed to be located at the Shackleton crater rim near the lunar south pole (latitude 89.9 degrees Southon the prime meridian) using the configuration shown in Fig. 5. Logistics resupply is assumed to arrive every 180days.

Figure 5. Simplified model of the Lunar base and its modules.

Each power module provides 105m2 of solar array surface and thus 10 kW of power available for the base in fullsunlight (BOL, approximately 21% efficiency for the panel), while regenerative fuel cells can assure up to 3 kW ofcontinuous power in eclipse phases. The full installed power generation capability of the system sums up to 26 kW,with a minimum of 6 kW continuous provision at all times and slightly below 20 kW nominal. This is more thanadequate for the model base with a nominal consumption estimated at 8 kW nominal for the habitat (6 kW for lunarnight operations) and 5 kW for laboratory and greenhouse. Degradation of the solar array surfaces is assumed at a rateof 2.5% per year to account for the harsh dust environment of the lunar surface.

From the above numbers, heat rejection requirements have been estimated at a maximum of 65 kW, where thelargest portion is encountered in the EPS modules due to energy conversion, distribution and storage. Dedicatedradiator elements therefore need to be placed at these elements, however, utilization of heat sinks on the surfacesuch as permanently shaded areas in the vicinity of the base will be analyzed further with the availability of the fulltopographic models. Similar to the above power considerations, a degradation of 2.5% per year has been estimated forheat rejection surfaces.

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V. Results and Discussion

The System Map model was conducted in Matlab on a 2.0Ghz computer, taking approximately 20-30 minutesfor offline analysis. Execution of the model was conducted in an online fashion, with estimations determined atapproximately 2Hz.

A. Validate Metric and FA Interactions

The first set of experiments demonstrate the feasibility of the approach by estimating metric and FAs, then scoring thedistance between them using Kullback-Leibler (KL) divergence.14 The purpose of this also is to determine the bestnumber of modes (i.e., mixtures in the GMM), based on the minimum number of modes and the minimum distance.Fig. 6 shows how the average distance between FAs, metrics, and their estimates changed based on the number ofassumed modes. Therefore, 10 modes were used for the remainder of this study.

Figure 6. KL divergence score of different modes shows that there are several local optima, with 10 modes having the least differencebetween data and the model estimates.

System Map estimation accuracies for both FAs (Fig. 7) and metrics (Fig. 8 of mission critical FA of “PersonalSurvivability”) were within 95% with anomalies at time t = 1100 and t = 2600. These anomalies occur due tochanges in GMM mixture where the mode’s data scenario is very different than the prior mode’s mean, but quicklyrecovers with new information. Fig. 9 shows how the mode changes can reasonably correspond to sharp changes inthe data set. Within a single mode, the DBN converges in approximately 100 time steps.

Figure 7. Representative sample of nominal ECLSS behavior. FAs were estimated accurately by the System Map, with anomalies occurringimmediately after entering a new mode.

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Figure 8. Metric performances and estimations in the mission critical FA “Personal Survivability”. Nominal ECLSS behavior shown.

Figure 9. The mission mode switched several times during the simulation (dashed line) but never needed modes 6 and 7, which were outlierstates.

Fig. 9 also shows that of the 10 mission modes identified in model training, two were unobserved during run time(modes 6 and 7). Unobserved modes may also occur in training as outlier states, which are ignored by the modelduring runtime. If the size of a mode largest representative sample is smaller than the DBN convergence threshold, itis also identified as an outlier and ignored. After further investigation, modes 6 and 7 were identified as outliers.

Fig. 10 is a representative sample of metric and FA interactions within a single mission mode. With other modes,FA “Personal Survivability” interacted most often with metrics Hunger and Thirst, while setup conditions (the startingmode) was heavily influenced by Heat Rejection Balance.

B. Comparison

The next experiment took several different configurations and compared the FA scores, using the FA “Personal surviv-ability” as the mission critical FAs. This includes point failure and recovery of various of the ECLSS. For comparison,nominal performance of a base at Lunar Equatorial region was also tested. The equatorial base (0 degrees lat/long)was given no greenhouse. Table B briefly compares average performance scores between the options.

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Figure 10. Mode 9, which occurred in the nominal Shackleton test during the first 300 time steps. This mode demonstrates causal interac-tions can occur across different HLAs. It also shows that during this part of the mission, EPS state is the critical mission driver.

FA Personal Survivability PerformancesTest Mean Variance

Shackleton Base Nominal 0.7222 0.0037Equatorial Nominal 0.7930 0.0008

Shackleton O2 Generation Failure 0.3923 0.0074Shackleton CO2 Removal Failure 0.4692 0.0053

Shackleton Food/H2O Resupply Failure 0.5310 0.0010

Fig. 11 shows how the Shackleton Lunar Base SoS performed over time and how the performances reflected thefailures of different ECLSS subsystems. The Equatorial base appears to be a safer option for the crew in nominaloperations, although it is not clear yet whether it is due to larger consumable storage or because of the location.Nevertheless, Fig. 11 shows how the performances can be monitored over time for comparison and operations levelmission tracking.

Figure 11. Comparing scores of a single mission critical FA can be used to analyze different design options and subsystem failure/recoveryscenarios.

VI. Conclusions and Future work

This paper introduced a method of SoS modelling in the context of high level Lunar Base architectures. As prelim-inary work it showed how to form metrics and FAs, find their interactions, and conduct basic SoS level comparison. Asimple, baseline mission example of Personal Survivability was modeled as mission critical. Metrics and FAs chosen

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were fairly generic to this simple initial problem and remained valid under changes in environmental condition andsystem failure. Resulting estimations were highly accurate in the examples given, showing the potential of the methodto solve more complex Lunar mission problems.

There are a few drawbacks to the approach. First, GMMs require conditioning to determine the best number ofmodes. Although it may be correct to assume that mission drivers are not known a priori, learning the interactionsbetween metrics and FAs are computationally expensive, due to a large search space (exponential on the number ofnodes). Therefore, modelling was conducted offline. Second, locally optimal solutions to GMMs and DBNs wereused, resulting in some accuracy losses for modes of very short duration.

The approach is significant for two reasons. First, it provides a framework to go from high level abstractionsfamiliar to mission planner and managers, down to the metric and functional attribute level, utilized by engineers.This allows design level comparison, enabling a space engineer the ability to choose between two competing (butalready mission satisfactory) designs. Second significance is its data driven nature. Future SoS Engineers and spaceengineers will need the ability to track metrics and FAs in telemetry. Data driven tracking is a prerequisite for bothplanning and real time SoS level decision making.

Reaching towards both goals (offline and online comparison), the next logical step in this research is to increasecomplexity and dynamic of the mission, by including lunar mining and active exploration. This will require a higherfidelity simulation to include more detailed operational data such as humans and robots movements. A monte carloapproach is needed to validate the full range of performance drivers allowing construction of metric spaces which aregenerically valid, applicable as a standard to all Lunar base designs for each class of mission.

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