Mode assessments for teamwork, checkmarks indicate the mode assessment of the expert.
\r\n\t
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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"64149",title:"Issues in the Probability Elicitation Process of Expert-Based Bayesian Networks",doi:"10.5772/intechopen.81602",slug:"issues-in-the-probability-elicitation-process-of-expert-based-bayesian-networks",body:'\nBayesian network (BN) is a mathematical model that graphically and numerically represents the probabilistic relationships between random variables through the Bayes theorem. This technique is becoming popular to aid in decision-making in several domains due to the evolution of the computational capacity that makes possible the calculation of complex BN [1]. Some examples of BN application areas are: software development project management [2, 3]; large-scale engineering projects [4]; and the prediction of success in innovation projects [5].
\nOn the other hand, there are open challenges related to the construction of BN. One of these challenges is to build the node probability tables (NPT). In cases where there are databases with enough information for the problem in question, it is possible to automate the process of constructing NPT through batch learning [6]. Unfortunately, in practice, in most cases, there is not enough data. That is, it is necessary to collect expert data and manually define the NPT [1].
\nFurthermore, experts can often understand and identify key relationships that data alone may fail to discover [7]. Therefore, the concept of smart data is defined by [7]: a method that supports data engineering and knowledge engineering approaches with emphasis on applying causal knowledge and real-world facts to develop models.
\nIn this context, it is necessary to manually elicit data from experts to define the NPT. However, given that the complexity of defining NPT increases exponentially, for large-scale BN, it becomes impracticable to manually define all the probability functions that compose each NPT [1]. In addition, experts often have time constraints and are rarely interested in manually defining NPT, partially because it is necessary to work with many probabilistic distributions for long periods [8].
\nIn addition, other factors may compromise the process of probability elicitation to construct the NPT, such as commonly used heuristics. Some well know heuristics used to reduce the cognitive effort in probability assessment task may lead the expert towards biased judgment of probability, leading to systematic errors. Moreover, the experts are hardly able to keep mutually consistent distributions during the NPT definition [1]. In addition, factors such as boredom and fatigue are enough to make the criteria deviate during probability assessment [8], when in fact, it should be uniformly applied throughout the whole elicitation process.
\nA solution to solve this problem has been proposed by [1], which will be referenced herein as the ranked nodes method (RNM). Its goal is to define the NPT of the parent nodes and then generate the NPT of the child nodes. Ref. [1] introduces the concept of ranked nodes, ordinal random variables represented on a monotonically ordered continuous scale. A fundamental feature of this method is that mathematical expressions generate the child node’s NPT. These expressions define the central tendency of the child node for each combination of states of the parent nodes and have as input a set of weights of the parent nodes, which quantifies the relative strengths of their influence on the child node, and a variance parameter.
\nAnother approach was proposed by [8], which will be referenced here as the weighted sum algorithm (WSA). This method uses well know heuristics in its favor, more precisely, the availability [9] heuristic and the simulation [10] heuristic. The main focus of this method is to assemble part of the NPT from experts by asking questions that comprehend cases that are easy to recall by experts, which is likely to be associated to more realistic probabilities. In the WSA, the remainder of the NPT is generated using interpolation techniques.
\nA systematic approach to generate NPT of nodes with multiple parents is proposed in [11]. This approach is an adaptation of the analytic hierarchy process (AHP) method for the task of probability elicitation and semiautomatic generation of NPT, in which the expert needs only to make the assessment of probabilities conditioned on single parents. In this approach, the probability assessment is indirect by means of paired state judgments and the NPT is generated through the calculation of the product of the probabilities of the child node conditioned on single parents.
\nThe three methods stated above reduce the burden for experts and allow the construction of complex BN in which manual elicitation of the NPT is unfeasible and, generally, there is not enough data to use batch learning. The reduced number of parameters to generate the NPT and consequently, reduced number of questions to ask the experts, makes it easier for the facilitator (e.g., BN expert) to deal with heuristics and possible biases during the NPT construction process. These methods can yet be extended with elaborate probability elicitation techniques (i.e., to improve its input).
\nTherefore, the objective of this research is to assess in detail three semiautomatic methods to generate NPT. We identified these methods in an exploratory study through a literature review. Additionally, we present heuristics that must be acknowledged during probability assessment for NPT construction and discuss extensions to these methods. It is our understanding that these methods can yet benefit from elaborate probability elicitation techniques. Such techniques can add additional overhead when manually defining the NPT, but this overhead is hugely reduced with semiautomatic methods (i.e., given the reduced number of questions to ask the experts) making them a viable choice to improve the method’s input.
\nThis chapter is organized as follows. Section 2 presents an introduction to BN. Section 3 presents common heuristics which should be acknowledged and considered during the probability elicitation process. Section 4 presents a probability elicitation technique which can extend some of the semiautomatic methods. Section 5 presents three semiautomatic methods to generate NPT. Section 6 presents our conclusions and future works.
\nBayesian networks are graph models used to represent knowledge about an uncertain domain [12]. The Bayesian network, \n
BN example.
In the above example, the probability of a person having cancer is calculated according to two variables: “Relatives had cancer” (\n
A challenge in constructing a BN is defining the NPT, which can be learned from data or elicited from domain experts. In practice, it is common not to have enough data for learning and elicitation from experts is the only option. However, the complexity of defining NPT grows exponentially, which makes the elicitation process costly and error-prone.
\nLet us consider the following example shown in Figure 2. In this BN, we want to assess Teamwork efficiency of a group of people that works collectively to achieve certain goals. Teamwork is directly influenced by Autonomy (i.e., self-management ability and shared leadership); Cohesion (i.e., the capacity of being in close agreement and work well together); and Collaboration (i.e., the ability to communicate and coordinate). This example will be used throughout this chapter.
\nBN example adapted from [15] where a child node Teamwork is influenced by three parent nodes: Autonomy (\n\n\nY\n1\n\n\n), Cohesion (\n\n\nY\n2\n\n\n), and Collaboration (\n\n\nY\n3\n\n\n). Each node has five ordinal states: very low (VL), low (L), median (M), high (H), very high (VH).
To elicit all the probabilities needed to construct the NPT of the child node Teamwork, a facilitator (e.g., BN expert) has to ask \n
Methods to address this problem were proposed. Noisy-OR and Noisy-MAX are two popular ones. However, the disadvantage of Noisy-OR is that it only applies to Boolean nodes. According to [1], the disadvantage of Noisy-MAX is that it does not model the extent of relationships required for large-scale BN. In this chapter, we present methods found in the literature that are applicable to a larger range of BN.
\nThe quantification process of a BN consists in converting expert knowledge, acquired through personal experiences, into probabilistic knowledge by eliciting a large number of subjective probabilities that reflect the expert’s belief at a given moment about something. Probability assessment can be described as the task of quantifying the chances of an event occur, using percentages. However, as the degree of complexity increases, it becomes increasingly difficult to size the probability of occurrence of each of the possible events in a given scenario.
\nFor instance, we may have a hunch as to who will be the winner of a particular tournament at a particular time, but we will never know for sure the exact probability since the number of factors that can influence the event goes beyond our reach. Apart from that, epistemic uncertainties (e.g., lack of knowledge about all the participants in the tournament) and aleatory uncertainties (e.g., possibility of a team losing a player) play an important role in probability assessment. Nonetheless, if asked, one is capable of making an evaluation and give a quick answer. How do people manage to judge the probability of highly uncertain events?
\nAccording to [16], people make use of a limited number of heuristics, mental shortcuts, to reduce the complexity of judging the probability of an uncertain event. These mental shortcuts reduce the cognitive effort required to judge the probability of such events. However, they can lead to biases that result in systematic errors. In [16], three commonly used heuristics are presented: representativeness; availability; and anchoring.
\nThe representative heuristic [16] describes the process by which people use the similarity of two events to estimate the degree to which one event is representative of another. It is used to answer questions such as: What is the probability that an event A originates from a process B? What is the probability of a process B generating event A? That is, if A is highly representative of B, the probability of A generating B is considered high. Conversely, if A is not representative of B, the probability of A originating from B is low.
\nConsider the following example adapted from [16]: “Steve is very shy and withdrawn, has little interest in people, or in the real world. He has need for order and organization, and a passion for details”. Based on this description, what is Steven’s most likely profession? Farmer or Librarian? You probably thought of a librarian. That happens because the probability of Steve’s profession be a librarian is evaluated by the degree to which he is representative, or similar to, the stereotype of a librarian. However, several other factors that should have a significant effect on probability, like the prior probability, or base-rate frequency of the outcomes have no effect on representativeness. For example, the fact that there are many more farmers than librarians should be considered in this case, but it is neglected.
\nThe availability heuristic [9, 16] is related to the judgment of probability of events occurring based on the ease with which we retrieve instances of these events in our mind. For example, to evaluate the likelihood that a person under the age of 30 years will suffer a heart attack, people usually do a quick search in their memory for cases they know of young people who have suffered a heart attack. This heuristic is useful because instances of larger classes are easier to remember than instances of smaller classes. However, the availability is affected by factors other than the frequency of events or probability. One may overestimate the probability of a young person getting cancer based on how recent an instance of such an event has occurred in his life, for example.
\nAnchoring and adjustment heuristic [16] occur when people judge probabilities based on an initial value, which is adjusted until the final response is reached. The problem with this heuristic is that the adjustments are usually insufficient. In other words, the expert assessment is likely to fluctuate around the initial anchor provided. It is important noting that, an anchor may be embedded in the formulation of a question to the domain expert (i.e., when a starting point is given), but it can also be the result of an incomplete computation.
\nIn short, heuristics are mental shortcuts that reduce the cognitive effort in the task of reasoning about the probability of events with uncertainty. Although useful, it has its disadvantages that must be considered in the knowledge elicitation process. Therefore, it is imperative to acknowledge the possible biases derived from heuristics during the process of probability assessment, explicitly informing the experts of their existence and adopting appropriate methods to reduce their effects.
\nThe number of probabilities to be elicited to construct an NPT may inevitably fall under some bias considering the effort needed from the experts. The semiautomatic methods reduce the number of questions to be asked to the expert or entirely removes the need of direct evaluation of probabilities during the construction of the NPT, which makes it easier for the facilitator and the expert to deal with these heuristics during the elicitation process, seizing the benefits of the heuristics and reducing their possible negative effects.
\nThe process of probability elicitation can be supported by a variety of techniques designed to aid experts when they find it hard to express their degrees of belief with numbers. These methods are based on setting-controlled situations in which probability assessments can be inferred from the expert’s behaviors [17]. In this section, we describe the use of probability scales with visual aids to make probability assessment easier for experts. However, it is worth noting, visual aids like probability scales (i.e., which uses numbers) still tend to be biased.
\nIt is our understanding that the use of visual elements such as probability scales can improve the input quality of semiautomatic methods (i.e., the ones which needs probability distributions as input), but indirect methods, which we do not discuss here, may improve the input quality as well. Several methods for indirect elicitation of probabilities have been developed. Some well know methods are: the odds method; the bid method; the lottery method; the probability-wheel method; among others [17, 18], these methods allow the extraction of probabilities without have to explicitly mention probabilities, so to speak.
\nBoth direct and indirect methods can be incorporated at some degree into semiautomatic methods. The purpose of this section is to show one of these techniques which can extend semiautomatic methods, as an example. Also, different techniques may produce different results, so we encourage readers to check a comprehensive review of issues related to the probability elicitation task which has a section dedicated for direct and indirect methods [17].
\nA probability scale is composed of a line that can be arranged vertically or horizontally with discrete numerical anchors which denotes the probabilities. It is a direct probability assessment method. To assess a probability, the experts mark a position on the scale. The probability value is given by the marking distance to the zero point of the scale. An example of a numerical probability scale can be seen in Figure 3.
\nProbability scale with numerical anchors.
There is no standard scale. For instance, anchors may vary in distance and values according to the domain, and lines can be arranged in different positions. Moreover, during probability assessment, one can use both numerical and verbal anchors. In [19] it is proposed a double scale that combines numbers and textual descriptions of probability to aid in the communication of probabilities. According to [19], verbal descriptions commonly used by people to express probabilities are directly related to the numerical values of the probabilities itself. In Figure 4, we can see an example of a double scale arranged in the vertical position with numerical and verbal anchors.
\nProbability scale with numbers and words.
The advantage of using a scale is that it allows for the domain experts to think in terms of visual proportion rather than in terms of precise numbers. However, it is important to consider bias that may be introduced using probability scales. For example, let us say an expert is requested to indicate several assessments on a single line. In such a case, he is likely to introduce bias towards esthetically distributed marks. This bias is known as the spacing effect [17] and can be easily avoided by using a separate scale for each probability. Another bias that may be introduced by the use of probability scales is the tendency of people to use the middle of the scale. This bias is known as the centering effect [17].
\nFurthermore, scales can be used in combination with other components that may help in the task of probability assessment. In [20], a method is presented for elicitation of a large number of conditional probabilities in short time. This method was used to build a real-world BN for the diagnosis of esophageal cancer with more than 4000 conditional probabilities. This BN predicted the correct cancer stage for 85% of the patients [21]. The main idea of this method is to present to the expert a figure with a double scale and a text fragment for each conditional probability. An example of combining probability scales with other components can be seen in Figure 5.
\nText fragment combined with a double scale for probability assessment.
On the left side is a text fragment describing the conditional probability to be assessed. On the right side, we have the double scale proposed in [19]. The text fragment is stated in terms of likelihood rather than frequency which circumvents the need for mathematical notation of the conditional probability. According to [21], the frequency format has been reported to be less liable to lead to biases and experts may experience considerable difficulty understanding conditional probabilities in mathematical notation. Conversely, such an approach may be less intuitive for domains in which it is difficult to imagine 100 occurrences of a rare event.
\nNonetheless, in [20], the fragments of text and associated scales are grouped up accordingly to the conditional probability distribution. In so doing, domain experts can assess probabilities from the same conditional probability distribution simultaneously. In other words, the centering effect is avoided by presenting all the related probabilities (i.e., from the same probability distribution) at once for the expert to assess. This approach considerable reduces the number of mental changes during the probability elicitation process. In regards to the spacing effect, the proposed method avoids it by using a separated scale for each probability.
\nIn this section, we present three methods to generate NPT that ease the burden for experts during the quantification process of a BN. These methods allow the construction of large-scale BN. The first is the RNM, which completely eliminates the need for direct probability assessment. The second is the WSA, which is based on two heuristics and needs only part of the NPT to be elicited from the expert. The third is an adaptation of the analytic hierarchy process (AHP) which reduces the cognitive effort, biases and inaccuracies from estimating probabilities to all combinations of states of multiple parents at a time. From now on, we will reference the latter as simply AHP. These three methods attack the magnitude problem of building NPT.
\nIn [1], the ranked nodes method (RNM) is presented. In this chapter, it is introduced the concept of ranked nodes, ordinal random variables represented on a continuous scale ordered monotonically in the interval [0, 1]. For example, for the ordinal scale [“Low”, “Medium”, “High”], “Low” is represented by the interval [0, 1/3], “Medium”, by the interval [1/3, 2/3], and “High”, by the interval [2/3, 1]. This concept is based on the doubly truncated Normal (TNormal) distribution.
\nA normal distribution is made of four parameters: \n
Examples of TNormal.
In this method, \n
Fenton et al. [1] do not present the details to, in practice, implement the solution. Despite presenting the mixture functions, there is no information regarding the algorithms used to generate and mix TNormal, define samples size and define a conventional NPT given the calculated TNormals. The latter enables the integration of ranked nodes with other types of nodes such as Boolean and continuous, which brings more modeling flexibility.
\nIn [22], it is proposed a probabilistic algorithm for this purpose, composed of two main steps: (i) generate samples for the parent nodes and (ii) construct the NPT. In step (ii), for each possible combination of values for the parent nodes (i.e., each column of the NPT), the samples defined in the previous step are mixed given a function selected by the user and a TNormal is generated using the resulting mix and a variance defined by the user. An overview of the algorithm is shown in Figure 7.
\nOverview of the algorithm.
As already mentioned, a ranked node is conceptually represented by an ordinal scale, which is mapped to the continuous interval [0, 1]. Thus, it is represented as a set of uniform distributions. For an ordinal scale with three values (e.g., “Bad”, “Moderate” and “Good”):\n
For the example shown in Figure 8, the set of uniform distributions is composed of the union of three uniform distributions\n
Conversion from ordinal to continuous scale.
Figure 7 shows that the algorithm is composed of four collections: \n
The repository strategy is used for optimization purposes. First, it is registered in memory (i.e., in \n
For instance, for 100% “Good”, it is collected samples of a uniform distribution limited in the interval [2/3, 1]. In [22] it is empirically defined that using a sample size of 10,000 is enough to guarantee a margin of error less than 0.1%. Each sample is registered with meta-data regarding its configuration (i.e., number of states and \n
To mix the distributions, a random element from each sample of the parents is removed and used to calculate a resulting element using a given function. For instance, consider node A with two parents B and C. If we are calculating the probabilities of A for the combination “Low”-“High” and the selected function is \n
Afterwards, the set of calculated elements and the given \n
Accordingly, the inputs to generate the NPT of a child node are: a weighted expression capable of generating curves equivalent to distributions expected by the experts; a set of weights of the parent nodes; and a value for \n
Row | \nParents | \nTeamwork | \n||||||
---|---|---|---|---|---|---|---|---|
Autonomy | \nCohesion | \nCollaboration | \nVL | \nL | \nM | \nH | \nVH | \n|
1 | \nVL | \nVL | \nVL | \nX | \n\n | \n | \n | \n |
2 | \nVL | \nVL | \nVH | \n\n | \n | X | \n\n | \n |
3 | \nVL | \nVH | \nVH | \n\n | \n | \n | X | \n\n |
4 | \nVH | \nVH | \nVH | \n\n | \n | \n | \n | X | \n
5 | \nVH | \nVH | \nVL | \n\n | \n | \n | X | \n\n |
6 | \nVH | \nVL | \nVL | \n\n | X | \n\n | \n | \n |
7 | \nVH | \nVL | \nVH | \n\n | \n | \n | X | \n\n |
8 | \nVL | \nVH | \nVL | \n\n | \n | \n | X | \n\n |
Mode assessments for teamwork, checkmarks indicate the mode assessment of the expert.
First, let us consider the rows 1 and 4, where all the parent nodes are in the highest and lowest states respectively. As can be seen in Table 1, when o all the parent nodes are in the lowest or highest states, the mode of the child node is also the lowest or highest state. Such a probability distribution can be obtained by any of the weighted expressions.
\nNow, let us consider the row 1 as the initial state, rows 2, 6 and 8 indicate that when the state of a single parent node shifts from lowest to highest state the mode of the child node shifts towards the highest state. Similarly, consider row 4 as the initial state, rows 3, 5 and 7 indicate that when the state of a single parent node shifts from highest to lowest state, the mode of the child node also shifts towards the lowest state.
\nHowever, it is quite clear that the shift effect is stronger when it occurs from the lowest to highest state. Hence, Table 1 reveals that the mode of the child node is inclined to go more towards the highest than lowest states which makes the \n
The process to determine the weights of the parent nodes and the variance parameter is not as straightforward as to determine the weighted expression. There is no guideline in the literature, as far as we know, to aid in this task. Nonetheless, one can use the mode assessments in Table 1 as a starting point to define the weight of the parent nodes. For instance, considering \n
Finally, let us consider row 1 as the initial state, rows 2, 6 and 8 indicate that the parent nodes have different strengths of influence on the child node. That is, when the parent node Autonomy shifts from lowest to highest state the mode of Teamwork slightly shifts towards highest states, however, the shift is higher when the state changes in the parent node Collaboration, as can be seen, if one compares rows 2 and 6. A similar effect is observed when comparing rows 6 and 8. Hence, it is derived from Table 1 the following constraint: \n
This method solves the magnitude problem of constructing NPT in complex Bayesian networks. On the other hand, a drawback to this method is that the domain context needs to fit a pattern that can be modeled by one of the weighted expressions. This solution has been validated through case studies in different real-world domains, such as human resources management in software projects [24], software quality forecasting [25], air traffic control [26] and operational management [27].
\nIn [8] the WSA method is proposed. This work introduced the concept of compatible parental configuration. The availability heuristic and the simulation heuristic are the base for this concept. As previously stated, the availability heuristic operates under the assumption that is easier to remember events that are more likely to occur. The simulation heuristic, in turn, operates according to which people determine the probability of an event based on how easy it is to simulate it mentally.
\nTo formally define the concept of compatible parental configuration, we take as a basis the work of [28]. Superscript is used to represent the states of a node and subscript to differentiate the parent-nodes. Therefore, consider that for \n
The compatible parental configurations are captured during the elicitation process by asking the domain experts to choose off the top of their head a plausible combination of states for each \n
relative weight (between zero and one) for each parent node, denoting its degree of influence on the child node \n
\n\n
where \n
For instance, let us consider the Bayesian network shown in Figure 2 where we wish to assess teamwork. For the sake of simplicity let us say that all the parents have the states “Low”, “Medium” and “High” instead of the five states from the original example. With WSA 3 × 3 distributions are needed to construct a complete NPT against \n
When the domain expert provides 3 probability distributions over the node \n
With the weights and 3 probability distributions over the node \n
In such a case, the probability of Teamwork (X) = “Low” conditioned to Autonomy (Y1) = “Low”, Cohesion (Y2) = “Medium”, and Collaboration (Y3) = “High” would be given by:
\nThis summarizes the WSA method, for an in-depth description please check [8]. Unfortunately, [8] do not describe how to deal with situations where the expert cannot select a single compatible parental configuration. Hence, an extension to this method is proposed by [29] to deal with such situations by averaging the probabilities of valid compatible parental configurations that experts might select.
\nAlthough the direct assessment of probabilities in the construction of NPT is feasible for small Bayesian networks and relatively simple domains, for medium to large networks the complexity and burden for experts grows substantially. As the number of parents and states increase, the more difficult it becomes for experts to reason about conditional probabilities with multiple parents and multiple combinations of states at once, and the more susceptible it becomes to biases and inaccuracies [11].
\nIn [11] it is proposed a systematic approach for generating conditional probabilities of nodes with multiple parents. It is an adaptation of the AHP method for the task of probability elicitation and semiautomatic generation of NPT where the expert only needs to provide probability assessments (i.e., indirect) conditioned on single parents. In this approach, the probability assessments are extracted from pairwise judgments of the states. The NPT is generated through the product of the probabilities of the child node conditioned on single parents.
\nBefore using the proposed method [11] it is required to define an agreed upon scale to perform the pairwise judgments over the states of the node. Saaty’s scale [30] can be used for this purpose or a custom one can be created. A good example of how to obtain a scale can be consulted in [19] in which four successive experiments were performed to generate a scale with numbers and words. The Saaty’s scale has nine values as seen in Table 2.
\nScale | \nDefinition | \nExplanation | \n
---|---|---|
1 | \nEqual likely | \nEvent A and evet B are equal likely | \n
2 | \nWeak or slight | \n\n |
3 | \nModerate more likely | \nEvent A is moderate more likely than event B | \n
4 | \nModerate plus | \n\n |
5 | \nStrong more likely | \nEvent A is Strong more likely than event B | \n
6 | \nStrong plus | \n\n |
7 | \nVery strong more likely | \nEvent A is very strong more likely than event B | \n
8 | \nVery, very strong | \n\n |
9 | \nExtremely more likely | \nEvent A is extremely more likely than event B | \n
Scale for the pairwise comparisons.
For a better understanding of the method, we substitute the original terminology used in the AHP for terms more appropriate to the probability context. Thus, the term attribute is replaced by event and the term importance is replaced by likelihood. To obtain prior probabilities pairwise comparisons of all states of the node are performed. Since each state is compared to every other state we can assemble a comparison matrix. In Figure 9 we see an example of a comparison matrix used to define prior probabilities of a node.
\nComparison matrix for prior probability elicitation of a node \n\nX\n\n.
In the above matrix, \n
The relative priority of \n
\n\n | \n1 | \n2 | \n3 | \n4 | \n5 | \n6 | \n7 | \n8 | \n9 | \n
\n\n | \n0 | \n0 | \n0.58 | \n0.90 | \n1.12 | \n1.24 | \n1.32 | \n1.41 | \n1.45 | \n
Random consistency index where \n
Similarly, to obtain the probabilities of a node \n
Comparison matrix of a node \n\nX\n\n conditioned on a single parent \n\nY\n\n in the state \n\n\ny\n\ns\nj\n\n\n\n.
In the above matrix \n
Resulting NPT for a single parent node.
The approach to generate the conditional probabilities for multi-parent nodes is based on [32], which states that when a node A in a Bayesian network has two parents B and C, its conditional probability in B and C can be approximated by \n
This approach focuses on easing the burden for experts by automatically generating probabilistic distributions of nodes with multiple parents, and consequently, the complete NPT through the calculation of the product of the probabilities conditioned on single parents. Thus, the expert assesses the probabilities of a particular child node conditioned to each of its parents, one at a time, and these probabilities are combined to get the node’s conditional probability conditional on all its parents.
\nIn [31] a similar method is proposed, also based on the AHP, which allow the quantitative evaluation of the inconsistency of experts in the task of probability assessment. The difference of the proposed methods is that in [11] the magnitude problem to construct NPT is reduced with a semiautomatic approach for the generation of the NPT and the cognitive effort is reduced because the experts only need to evaluate, indirectly, probabilistic distributions conditioned on a single parent at a time, whereas in [31] the effort is even greater than the direct elicitation of probabilities. Nonetheless, it is our understanding that the method proposed in [31] can somewhat extend other methods such as the WSA, without causing too much overhead. However, further studies are needed to confirm this.
\nDespite recent popularity, the construction of BN is still a challenging task. One of the main obstacles refers to defining the NPT for large-scale BN. It is possible to automate this process using batch learning, but it requires a database with enough information. In practice, this is not common. The other option is to elicit data from experts, which is unfeasible in most cases due to the number of probabilities required. A third option is to use semiautomatic methods that given an input (i.e., elicited from experts) generates the NPT.
\nIn this chapter, we present three semiautomatic methods, found in an exploratory study through a literature review. These methods help, to a certain extent, to minimize the effects of human biases by reducing the parameters that are required to construct complete NPT. However, these methods are highly reliable on the input data elicited from experts. Therefore, flawed input necessarily produces nonsense output. For this reason, we present one of many probability elicitation techniques as an example, which can improve the input data needed by the semiautomatic methods and reduce the garbage in/garbage out effect.
\nThe biggest problem with elaborated probability elicitation techniques is undoubtedly its cost, which is often greater than the direct elicitation of probabilities. Thus, these methods are not well suited for the construction of large-scale BN, despite been useful to deal with well know biases. However, it is our understanding that the cost to use elaborated probability elicitation techniques is drastically reduced when only is needed to elicit a small fraction of data of what would be necessary for manual definition of NPT. Therefore, the combination of semiautomatic methods and elaborated probability elicitation techniques might help building more reliable BN.
\nFor example, let us consider the WSA method that uses a partial elicited NPT to generate a complete one using the concept of compatible parental configurations, weights of the parents and a weighted sum algorithm. Once the compatible parental configurations have been chosen, its probabilities can be elicited using a sophisticated probability elicitation technique with a rather small overhead. In one way, the probability elicitation technique becomes feasible and, theoretically, the input of the semiautomatic method is improved.
\nNonetheless, it is evident that some methods may benefit more from elaborated probability elicitation techniques than others. However, it is still possible to use these techniques even in a method such as RNM. For example, the expert can inform the probabilities rather than the mode of each probabilistic distribution of the combination of extreme states (see Table 1). We believe that studies must be carried out to check if combining elaborated probability elicitation techniques with semiautomatic method can indeed improve the construction of large-scale BN.
\nDielectric elastomer actuators (DEAs) are currently used in a variety of applications such as robots and medical devices. Since a DEA is very light and capable of high output, it is expected to be able to control the output of the planetary exploration ship and the solar panels loaded on exploration ships.
\nWe are developing a DEA related to the output and control of Mars probes that observe the surface of Mars. Mars Airplane is a new Mars observation platform that enables a wide range of observations from low altitudes. Since 2010, the Japanese Mars spacecraft working group has been working on the conceptual design of Mars airplanes and various basic researches [1, 2, 3, 4, 5]. Mars exploration is performed with a weight of 6 kg, a wing width of 2.4 m, and a maximum cruising speed of 70 m/s. We are developing such a machine, as shown in Figure 1 [6].
\nImage of the Mars exploration airplane.
We would like to take this airplane down from the Mars exploration spacecraft with a parachute, disconnect the parachute at a high altitude (30 km) on Mars, control its flight remotely, and then gradually lower the altitude to fly a distance of about 300 km. Therefore, it is necessary to avoid high mountains on flights after the middle stage.
\nThis Martian plane can obtain more detailed data than satellites and can observe a wider range than rovers. Also, one of the unique features of the Mars plane is to observe the formations of the canyons. Satellites cannot see the formation from the sky, and rovers cannot approach them.
\nFlight exploration by Martian planes has some difficulties, as detailed below:
\nThese planes are not mass-produced and are very expensive due to their special payload and avionics for academic research. In addition to this, Mars planes must be lightweight to fly in the thin atmosphere of Mars. It also has to be fairly lightweight to carry this spacecraft to Mars as well as to even be transported to Mars itself.
\nDEAs have the potential to be used as actuators for control surfaces (i.e. ailerons, rudder, and elevator) and as a propeller for the Mars airplane, since it is light and has high output and high efficiency. Another advantage of the DEA is that it is linearly driven, making it less susceptible to dust. This research investigated the feasibility of the DEA for the application of control surfaces (i.e., ailerons, rudder, and elevators) on the Mars airplane. A structural model of a wing having the control surface, the DEA, and a linkage was built, and a wind tunnel test of a control surface actuation using a DE actuator was carried out to investigate the feasibility of the DE actuators for the Mars airplane.
\nThe results obtained in this study will be useful not only for the development of Mars exploration airplanes, but also for the structure and aerodynamic design of lightweight airplanes where large aerodynamic deformation is expected. The study also provides valuable examples of some of the expensive custom-made airplanes for academic research, airplanes that are not capable of many flight tests, and airplane development processes for which conducting flight tests are difficult.
\nTo date, various types of soft actuators have been studied, and many functions desirable for different devices have been studied [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]. An especially attractive soft actuator is the dielectric elastomer (DE). DEs began to be studied in 1991 by R. Pelrine, S. Chiba et al. [16].
\nThe basic element of a DE is a very simple structure comprised of a thin elastomer sandwiched by stretchable and flexible electrodes (see Figure 2) [24]. When a voltage difference is applied between the electrodes, they are attracted to each other by Coulomb forces leading to a thickness-wise contraction and plane-wise expansion of the elastomer. The typical thickness of the elastomers is about 500 microns to 1 mm. The electrode uses carbon black, CNT, or nano-sized metal. At the material level, the DE actuator has a fast speed of response (over 100,000 Hz), with a high strain rate (up to 680%), as shown in Figure 3, a high pressure, and a power density of 1 W/g [32, 33, 34]. DEs can also be used for pressure-sensors and 3D position-sensors.
\nPrinciple of operation of DEs.
Expanding Circular Actuator up to 680.
As shown in Figure 4, recently, DE actuators having only 0.15 g of DE material have been able to lift a weight of 8 kgf easily using the single wall carbon nano tube (SWCNT) electrodes (ZEONANO®-SG101) [33]. With 0.15 g of DEs, it is possible to lift an 8 kg weight by 1 mm or more. Its operating speed is 88 ms.
\nA DE lifted a 8.0 kgf weight using SWCNTs (ZEONANO®-SG101) (ZEONANO®-SG101 is a single-wall carbon nanotube synthesized by the Super-Growth method. (Diaphragm type DE actuator having a diameter of 8 cm)).
When the DE sheet is rolled, it becomes an actuator that looks like a human muscle. Figure 5 shows the roll actuators with 3-DOF [34]. As shown in Figure 6, a DE can be the arm or leg of a robot. Using five of them, we created a robot that can moves around the surface of Mars [34], so it enables sideways stepping like a crab without turning around, when it collides with wall.
\nRoll actuator having 3-DOF.
Biologically inspired robots powered by DE rolls.
These roll-type actuators seem to be ideal for moving the antenna or solar panel of a space craft to the correct position and as an actuator for a working robot arm on it. For example, a robot arm is attached to the Japanese experimental module Kibo of the International Space Station (see Figure 7). It is possible to use DEs as the drive source.
\nInternational Space Station: Kibo (Japanese experiment module) has a robot arm.
In order to verify the possibility of using a DEA as a surface control actuator for the Mars exploration airplane, a wind tunnel was used to operate with the DEA while receiving wind.
\nUsing a continuously circulating low-speed wind tunnel (see Figure 8) owned by JAXA (Japan Aerospace Exploration Agency), we conducted a verification experiment to verify whether the DEA actuator could be used as a steering actuator under the wind received during flight. The wind tunnel used in this experiment has a measurement section of 2 m x 2 m and a maximum wind speed of 67 m / s (up to 60 m/s during continuous operation using the model).
\n2 m x 2 m Low-speed wind tunnel.
In the preliminary study, the wind speed was set from 0 m/s to 40 m/s in order to match the actual driving conditions as much as possible. In addition, it was decided to observe the aileron driving state by changing the angle of attack from 0° to ±10° at 5° intervals at each wind speed (Figure 9).
\nInput parameters.
The structural model of the wing used in the experiment was shaped vertically so that the surface control actuator (in this case, an aileron-like structure) can be driven by the DEA in a limited space in the wind tunnel. The body is shown in Figure 10 [6].
\nBody used in experiment.
The dimensions of the wings used in this experiment were 168.5 mm wide, 633 mm high and 25 mm thick, and the dimensions of the ailerons were 78.5 mm wide and 633 mm high. The wings and ailerons were made using polycarbonate resin for the frame and ABS resin for the exterior. The bottom of the model was 125 mm in diameter and 757.5 mm in length. The tip and tail are made of ABS resin, and the center is made of acrylic resin. For strength, the parts are reinforced with aluminum. The aileron has a hollow structure, but the total weight was about 5 kg. A DEA to control ailerons was installed inside the body. The DEA and aileron are connected by a link mechanism built into the main body (see Figure 11) [6], and when the DEA is displaced by 2 mm, the aileron moves 20 degrees. The DEA unit for aileron drive has a structure that adopts a diaphragm type with an outer dimension of φ100 mm.
\nLink mechanism between the body and the measurement equipment.
As shown in Figure 12, a load measuring device other than the main body, a high-voltage power supply, a high-voltage switch, etc. were installed outside the wind tunnel and connected to the main body with a cable so as not to obstruct the air flow in the wind tunnel [6]. A video camera was installed on the ceiling outside the wind tunnel to observe the state of the enclosure, and the images were taken from the observation window.
\nSystem diagram of the aileron drive experiment with a DEA.
First, in order to examine the specifications required to control the actuator used to steer the aileron, a load cell was used to measure the load applied to the actuator part at each steering angle. Figure 13 shows the measurement system used for load measurement [6].
\nLoad measurement system using a load cell.
The load cell used for load measurement was mounted at the DEA mounting position of the main body. The maximum load applied to the load cell is 20 kg, and the analog data output from the load cell is converted to digital data by the 24-bit A/D converter IC (HX-711), and the CPU (ATmega328P). A lithium polymer battery (Li-Po) was used as the power source to minimize the effect of noise on the weak signal output from the load cell. In order to shorten the connection distance, the circuit to the CPU was attached to the fuselage. A personal computer for operation and recording was installed outside the wind tunnel, and it was connected by serial communication.
\nA laser distance sensor (VL50L0X) was also installed to measure the displacement velocity (Figure 14) [6]. Since this laser distance sensor uses I2C for the interface, it is not easily affected by noise and stable measurement is possible. The control was performed by the same CPU (ATmega328P) as the load measurement, and the measurement data was transmitted to the measurement PC by serial communication. Laser distance sensors were installed in the front and rear to observe the movement of ailerons and the DE.
\nLaser distance sensor system installed inside the body. (a) Mounting location of the laser distance sensor; (b) Laser distance sensor system.
The load was measured by continuously changing the wind speed from 0 m/s to 40 m/s in 5 m/s increments and setting the steering angles to 0, 5, 10, 15, and 20 degrees. When the set wind speed was reached, measurements were taken at each wind speed for about 30 seconds, and the load applied to the actuator section was measured (see Figure 15) [6].
\nLoad applied to the actuator section (by steering angle and wind speed).
In this experiment, it was found that the DEA was loaded with 11.54 kg/f in an environment with a steering angle of 20 degrees and a wind speed of 40 m/s (see Table 1). In order to move the aileron through the link mechanism, a force of about 2.6 kgf is required even in the absence of wind. It was found that a force of about 14.14 kg/f is required to steer 20 degrees in an environment with a wind speed of 40 m/s. It was also confirmed that the wings were deformed from the joint with the airframe at a wind speed of 30 m/s or more. Since the experiment was repeated in such a state and there was a risk of damage to the blade due to fatigue, the aileron drive experiment with the DEA was carried out at a wind speed of 0 m/s to 30 m/s. In order to steer 20 degrees in this environment, a DEA that can obtain a force of about 8.7 kg/f is required.
\n\n | Wind speed (m/s) | \n|||||||
---|---|---|---|---|---|---|---|---|
5 | \n10 | \n15 | \n20 | \n25 | \n30 | \n35 | \n40 | \n|
Load applied to the actuator (kg / f) | \n0.12 | \n0.37 | \n1.12 | \n2.30 | \n3.90 | \n6.10 | \n8.72 | \n11.54 | \n
Load applied to the actuator section at each wind speed when the rudder angle is 20 deg.
The load cell mounted for load measurement was replaced with a diaphragm type DEA, and an aileron drive experiment was conducted. Figure 16 shows the state of the DEA mounting.
\nDEA mounted in the body. (a) Diaphragm type DEA. (b) DEA built into the body.
The DEA unit used had a donut shape with an outer diameter of φ100 mm, a DEA part with an outer diameter of φ80 mm, and a central part of φ50 mm (see Figure 15a). The DEA used a 3 M acrylic sheet (VHB4910) as the main elastomer and SWCNT (SG101) manufactured by Zeon Corporation as the main electrode material. This DEA unit had a displacement performance of 2.0 mm with an applied voltage of DC 3.2 kV under a load of 4.0 kg, and the drive time at this time was about 100 ms. The DEA was driven by a high voltage power supply and a high voltage switch located outside the wind tunnel. The high-voltage power supply installed outside the wind tunnel and the DEA installed in the enclosure are connected by a high-voltage cable with a length of about 6 m. However, due to the low current consumption of the DEA, the maximum voltage drop during driving is 100 V, which is within the range where there is no problem in driving the DEA. The DEA unit consists of four cartridges, and if one of the DEA cartridges fails, the remaining DEA cartridges can drive it.
\nIn this experiment, the wind speed was changed from 0 m/s to 20 m/s every 5 m/s, and the change in wind speed at each wind speed was recorded with a video camera installed on the ceiling of the wind tunnel. The rudder angle was measured by analyzing the recorded video.
\nIn the initial experimental plan, the angle of attack was planned to be changed from −10° to +10° in 5° increments, but the stress applied to the wing was greater than expected, so there was a risk of damage to the skeleton. In order to avoid such an outcome, this time, the angle of attack was set to 0° only, and the wind speed was changed from 0 to 20 m/s at 5 m/s intervals.
\n\nTable 2 shows the aileron angle at each wind speed. Figure 17 shows the aileron displacement at each wind speed [6]. Up to a wind speed of 5 m/s, the aileron angle could be obtained up to 20 deg. However, the aileron angle gradually decreased from a wind speed of 10 m/s and reached 4 deg. at a wind speed of 15 m/s.
\n\n | Wind speed (m/s) | \n||||
---|---|---|---|---|---|
0 | \n5 | \n10 | \n15 | \n20 | \n|
Aileron angle (deg.) | \n20 | \n20 | \n9 | \n4 | \n0 | \n
Aileron angle at each wind speed.
Aileron displacements at applied voltage DC3,200 V.
\nFigure 18 shows the aileron drive speed when there is no wind, as measured in the lab. The rudder angle could be moved up to 20° at a speed of about 100 ms, and the same rudder angle and speed could be reproduced even if the drive control was repeated.
\nAileron drive speed when there is no wind.
\nFigure 19 shows the operating speed of the aileron. The displacement speed was measured using a laser distance sensor mounted inside the body. At a wind speed of 5 m/s, it took 250 ms to reach the maximum displacement, but at a wind speed of 10 m/s, it took 300 ms. As described above, since the angle change of the aileron can be easily replaced with the voltage change, the feedback control can be easily performed by changing the voltage applied to the DEA using the voltage change.
\nAileron’s operating speed measured by the laser distance sensor. (a) Wind speed of 5 m/s; (b) Wind speed of 10 m/s.
The structural model used this time required a force of 2.6 kg for steering even at a wind speed of 0 m/s. This was a huge loss. It is probable that the maximum aileron angle could not be obtained due to insufficient driving force at a wind speed of 10 m/s. Most of this loss was due to the link mechanism. By increasing the efficiency of the link mechanism, we were able to obtain a maximum displacement of up to 15 m/s even with the same DEA. In the next experiment, we will investigate how much the mechanism can reduce the power consumed by developing a new drive that drives ailerons directly, enabling a simple and practical steering system.
\nTo send a Martian plane to Mars, we need to dramatically reduce the weight of our compact and powerful motors. In addition, a powerful, efficient and responsive motor is essential for long-term flight of the spacecraft on the surface of Mars. Also, the surface temperature of Mars is very low and dust is present. Therefore, the required level of efficiency and responsiveness is very high. In this paper, based on the data obtained in this experiment, we attempted to compare the current level of a DEA with existing motors for these requirements.
\nFirst, we will explain the performance of the DE developed for this experiment:
\nThe total weight of the DEA used is 52.8 g, of which 51.8 g is the weight of structures, etc., and the weight of the DEA itself is as small as 0.98 g. This DEA can lift a 4 kgf weight by 2 mm with an applied voltage of 3.3 kV. In order to increase this operating speed, the DE has been strengthened, and the total weight is 0.98 g, which is 98 ms.
\nNext is a comparison between the DE and existing motors:
\nFrom the above data, the power of the DE linear actuator is 0.0074 W per gram. As shown above, the weight including the DE actuator and its associated structure was approximately 53 g. If a similar linear actuator is configured using an existing DC motor of similar weight, the output of the linear actuator is 0.0015 (W). The weight including the DC motor and linear gear is about 95 g. Therefore, the DEA has a working speed per gram that is 4.9 times faster than a linear actuator that uses an existing DC motor. However, in the case of a linear actuator that uses a DC motor, a displacement of 1 mm takes about 200 milliseconds, so the difference in drive time is 9.9 times. In this experiment, we created a DE actuator that can lift a weight of 4 kgf using SWCNT (ZEONANO®-SG101) from Zeon Corporation. However, using high-crystal SWCNTs (extracted in the laboratory of Zeon Corporation under the guidance of Chiba et al.) gives about 1.32 times better results [35]. An SEM photograph of high-crystal CNTs is shown in Figure 20. It is estimated that DE motors using this CNT are about 13.1 times better than existing motors. When using metal CNTs, it is estimated to be twice as high as SWCNTs with high crystallinity. It is expected to be about 27.5 times that of existing motors.
\nSEM photograph of high-crystal CNT.
In order to explain in more detail the good response of the DE obtained in this research, we compared it with the existing servo motor (which shows better performance than the model airplane used for radio control). The reason we chose the servo motor is that it can be controlled more accurately. The specifications of the servo motor that can obtain the same level of output as the DEA unit used this time are “servo motor (GWS): weight 41 g, torque 4.1 kg/cm, running speed: 270 ms /60 degrees”. In contrast, the DEA used this time weighs 36 g (when four cartridges are built in), is about 13% lighter than the servo motor, and has a drive speed of 98 ms/2 mm, so it can be driven at higher speeds.
\nBased on the data obtained, the power consumption of the DE will be explained as follows. The power consumption during driving was measured with a voltage/current monitor of a high-voltage power supply installed outdoors. The wind speed was 5 m/s, the applied voltage was 3.2 kV, and the power consumption was 0.29 W. The current at this time was as small as 0.09 mA, and there was almost no voltage drop or heat generation due to the wiring cable. As mentioned above, one of the features of the DEA is that it consumes less current and can contribute to the weight reduction of the wiring cable, that is, the weight reduction of the main body. The power consumption during driving was measured with a voltage/current monitor of a high-voltage power supply installed outdoors. The wind speed was 10 m/s, the applied voltage was 3.2 kV, and the power consumption was 0.29 W. The current at this time was as small as 0.09 mA, and there was almost no voltage drop or heat generation due to the wiring cable. One of the features of the DEA is that it consumes less current. It can also contribute to the reduction of wiring cables and reduce the weight of the aircraft.
\nConsidering the manufacturing cost of a DE, the weight of the DE including reinforcement is 0.96 g, which is cheaper and lighter than the price of a general existing motor with the same output. The SWCNT used as the electrode material for the DE in this experiment has started being mass produced at ZEON, so it costs about 1,000 yen ($ 9.6) per gram. Also, since the amount used is about 0.1 g, it is 100 yen (9 cents). The 3 M acrylic used for the elastomer is 20 yen per gram, so even if 1 g is used, it costs 120 yen ($ 1.15), which is cheap enough. Also, as mentioned above, the DEA itself is sufficiently lightweight and compact, which is a great advantage when mounted on a rocket.
\nWhen the DE is actually transported to Mars, it passes through outer space, so the effects of cosmic rays cannot be ignored. Next year, we plan to conduct a DE exposure test at the International Space Station (ISS: see Photo 7) and observe its effects.
\nFinally, we will explain the further improvement of the DE. As shown in Photo 4, we succeeded in launching a weight of 8 kg with a DE of 0.15 g. Using this, it will probably be able to move smoothly even in the wind with a higher speed. In this experiment, SWCNT (SG101) was also used, but it has been found also that the use of highly crystallized SWCNTs further improves drive speed and output. Even if the above link mechanism is not improved significantly, wind experiments of 25 m/s or more can be performed. In addition, new acrylics are currently being synthesized by Chiba et al. These acrylics can be used at −40°C to 150°C and may be able to handle even the harsh temperatures found on Mars. Also, due to the sufficient withstand voltage of the film, the control unit of the Mars probe will be developed mainly using this elastomer.
\nFrom the above experimental results, it is suitable for controlling the Mars probe because it can output a large amount of DE even with a small number of DEs and has a high operating speed. In addition, DEs are manufactured at low manufacturing cost and can withstand −40°C.
\nThus, for the first time in the world, we aim to fly in the atmosphere of Mars. By doing so, we would like to obtain our own Mars observation data such as high-resolution residual magnetic field data and atmospheric data. By establishing this technology, it will lead to the flight of other celestial bodies (Titan, Venus, etc.) that have an atmosphere.
\nThe function of detecting radiation on Mars (particle type, energy range, dose range, etc.) and the function of detecting underground features such as caves and water volume, which are important considerations for Martian colonies, have not been considered in the paper. At this moment, the payload of the airplane is small and we will not able to consider them. As mentioned in the background of DEs, however, the output of the DE has come to lift 8 kg against the weight of the 0.15 g DE. In the near future, we would like to increase the output of the DE, so that a larger payload can be realized.
\nDEs are also suitable for controlling the solar panels, antenna control, and drive output control of planetary exploration spacecraft.
\nWhat we need to know in the future is how well DEs can withstand cosmic rays. As early as next year, we plan to experiment with how a DE behaves in space on the International Space Station.
\nRecently, more and more research has been aimed at exploring the possibility of applying DEs to frequently used items such as spacesuits, power suits, and robots, and we hope that the results of this research will be valuable.
\nWe would like to thank to Mr. Hiroki Ura and Mr. Takashi Yajima of the Aerodynamics Research Unit, Japan Aerospace Exploration Agency (JAXA)\'s Ministry of Education, Culture, Science and Technology’s Advanced Research Platform Operation Promotion Project “Wind and fluid Engineering Platform” for their enthusiastic support in getting this important data using their wind tunnel.\n
We also thank Aisin AW Co., LTD. for its financial support and manpower support during measurement in the wind tunnel.
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