Fuzzy Role Based Expert System for Human Thermoregulation Model

........................................................................................................................................................ 3 INTRODUCTION................................................................................................................................................ 3 BASIC CONCEPTS OF FUZZY SETS AND FUZZY LOGIC .......................................................................... 4 Fuzzy Sets and Fuzzy Set Operations.................................................................................................................. 4 Fuzzy Relations.................................................................................................................................................. 5 Fuzzifier ............................................................................................................................................................ 5 Defuzzifier ......................................................................................................................................................... 5 UC BERKELEY MULTINODE HUMAN PHYSIOLOGY AND THERMAL MODEL................................... 6 Background........................................................................................................................................................ 6 Model Overview................................................................................................................................................. 6 Original Thermoregulation System ..................................................................................................................... 7 Fuzzy Controller ................................................................................................................................................ 8 Structure of Fuzzy Model/Control................................................................................................................... 8 Fuzzifier......................................................................................................................................................... 9 Membership Functions ................................................................................................................................... 9 Fuzzy Rule Base........................................................................................................................................... 10 Fuzzy Inference Engine ................................................................................................................................ 11 Defuzzifier ................................................................................................................................................... 12 Implementation ................................................................................................................................................ 14 RESULTS........................................................................................................................................................... 16 Initial Validation .............................................................................................................................................. 16 Performance of Fuzzy Controller ...................................................................................................................... 17 CONCLUSION .................................................................................................................................................. 19 FUTURE WORK ............................................................................................................................................... 19 REFERENCES: ................................................................................................................................................. 19 Fuzzy Role Based Expert System for Human Thermoregulation Model ME290M Final Project Spring 1999 Yitao Duan May 19, 1999 Abstract This paper investigated the application of fuzzy rule based expert system (FRBES) to the identification of human thermoregulation system which has long been modeled as a crisp controller without adaptation by earlier approaches. In this project, human body is treated as an adaptive fuzzy logic system. An additional fuzzy controller is implemented and its effect studied. A fuzzy IF-THEN rule base consisting of a set of intuitive fuzzy rules is constructed and applied to the fuzzy thermal controller.This paper investigated the application of fuzzy rule based expert system (FRBES) to the identification of human thermoregulation system which has long been modeled as a crisp controller without adaptation by earlier approaches. In this project, human body is treated as an adaptive fuzzy logic system. An additional fuzzy controller is implemented and its effect studied. A fuzzy IF-THEN rule base consisting of a set of intuitive fuzzy rules is constructed and applied to the fuzzy thermal controller. Introduction An important issue involved in the study of human thermoregulation system is understanding the controlling mechanism which regulates temperatures of all body parts. This system, due to the lack of quantitative data and the difficulty in observation, has not been fully understood. Almost all theories are on hypothetical level and most approaches model the controlling mechanism as a pure mechanical system. In Stolwijk’s[1] thermoregulation model, for example, deviation of temperatures in several body parts from their respective “set points” are used as error signals which generate control efforts by causing evaporative heat loss, heat production from shivering or changes in the peripheral blood flow in the appropriate locations in the body. All of these actions, in turn, form a nonlinear controller. This approach, although can be justified in certain thermal conditions, is only a greatly simplified version of what is actually going on inside human body and, inevitably, exhibits inability to emulate the correct response of human body in some conditions. Several things can be challenged. 1. Human body is adaptive. It is known that human body can adjust to its new thermal environment. Not only some of its physical properties, such as heat capacitance and conductance, can be variant, but also its thermoregulation mechanism. For example, Eskimos, who live in north pole region, cannot sweat. This is a long time adaptation to their environment. Living in such extreme cold condition, sweating is not only expensive in terms of energy but also dangerous. However, if they move to a warmer area, they will, eventually, regain their ability to sweat. 2. It is questionable whether human body adopts a “crisp” thermal control mechanism. Cold and warm are all perceptions and inherently fuzzy. Our knowledge on human sensor mechanism is still incomplete because it is not accessible to observation and study. It is unlikely that human body relies exclusively on numerical sensor input as a way to regulate its thermal states. 3. The so-called thermal comfort index, which has long been investigated but is still not clearly defined, is actually a fuzzy concept. Comfort is a fuzzy perception and the traditional “crisp” approach can hardly model it. This project tries to attack these problems by incorporating fuzzy logic into the human thermoregulation model. Basic Concepts of Fuzzy Sets and Fuzzy Logic Fuzzy Sets and Fuzzy Set Operations Fuzzy Set: Let U be a collection of objects of interest, and be called the universe of discourse. A fuzzy set F in U is characterized by a membership function μF: U →[ 0,1], with μ F(u) representing the grade of membership of u∈U in the fuzzy set F. A Fuzzy set can be viewed as a generalization of the concept of an ordinary set whose membership function only takes two values { 0, 1 }. Figure 1 shows member functions of three fuzzy sets, namely, “Cold”, “Neutral” and “Warm”, which are three common linguistic descriptions of thermal sensations. The universe of discourse is all possible environment temperatures, i.e. U = [Tmin, Tmax], where Tmin and Tmax are minimum and maximum temperatures of a certain thermal condition. Figure 1 Member functions of three fuzzy sets Support, Center, and Fuzzy Singleton: The support of a fuzzy F set is the crisp set of all points u∈U such that μ F(u) > 0. That is, SF := {u : u∈U,μ F(u) > 0 } The center of a fuzzy set F includes the point(s) with maximum member function values. CF := {u : u∈U,μ F(u) ≥ μ F(v), for all v∈U } If the support of a fuzzy set F is a single point in U at which μ F(u) =1, then F is called a fuzzy singleton. Intersection, Union, and Complement: Let A and B be two fuzzy sets in U, The intersection of A and B, A∩B is a fuzzy set in U whose member function is given forall u∈U by μ A∩B(u) = min { μ A(u), μ B(u) } The union of A and B, A∪B is a fuzzy set in U with member function defined forall u∈U by μ A∪B (u) = max { μ A(u), μ B(u) } The complement of A, denoted by A’, is a fuzzy set in U with member function defined forall u∈U by μ A’’(u) = 1 μ A(u) Note that the definitions of intersection, union and complement given here, when A and B are ordinary sets, are consistent with the corresponding definitions in conventional set theory. It should be mentioned that, however, this definition shows only one possible choice for these operations. The choice of operations corresponds to one’s Tmax Tmin Tset 1 Cold Warm Neutral interpretation of the meaning of these operations. Based on different interpretation ranging from intuitive argumentation to empirical or axiomatic justifications, other operators have been suggested in literature. T-norm: A T-norm, denoted by *, is a two place operation from [ 0,1 ] × [ 0,1 ] →[ 0,1] which includes fuzzy intersection, algebraic product, bounded product and drastic product, defined as min{ x, y } fuzzy intersection xy algebraic product max{ 0, x + y –1 } bounded product x if y = 1 y if x = 1 drastic product 0 if x, y < 1 where x, y are values of two fuzzy member functions. Fuzzy Relations Fuzzy Relation: Let U and V be two universes of discourse. A fuzzy relations is a fuzzy set in the Cartesian product space of U and V, U×V, and is characterized by a member function μ R’’(u,v): U×V →[0,1] indicating to what extent the relation is true. Sup-Star Composition: Let R and S be fuzzy relations in U×V and U×W, respectively. The sup-star composition of R and S is a fuzzy relation denoted by R ° S and is defined by μ R °S (u) = supv∈V{ μ R(u,v)* μ S(v,w) } where u∈U, v∈V, and * can be any operator in the class of T-norm defined earlier. It is clear that R ° S is a fuzzy set in U×W. Fuzzy relations and compositions are used to obtain the interpretation of fuzzy IF-THEN rules. Fuzzifier The fuzzifier maps a crisp point x∈U to a fuzzy set A in U. The most commonly used fuzzifiers are • Singleton fuzzifier: A is a fuzzy singleton with support x. That is, μ A(u) = 1 for u = x and μ A(u) = 0 for other. • Nonsingleton fuzzifier: μ A(x) = 1and μ A(u) decreases as u moves away from x. Fuzzifier is an essential part of a fuzzy system. It relates numerical information to fuzzy sets. Defuzzifier Defuzzifier performs a mapping from fuzzy sets in V to a crisp point y∈ V. There are different methods of doing so, each of which has its own suitable application. For details about defuzzifier, please refer to Li-Xin Wang [5] and Mohammad Jamshidi [7]. UC Berkeley Multinode Human Physiology and Thermal Model Background Stolwijk’s 25 node model of thermoregulation (Stolwijk and Hardy 1966) set out the fundamental concept, algorithm, physical constants and physiological control sub-systems for many contemporary multinode models (Hwang and Konz 1977). The Berkeley Multinode Comfort Model is based on the Stolwijk model as well as on work by Tanabe in Japan (Tanabe, Stuzuki et al. 1995), but includes several significant improvements over the Stolwijk model. The Stolwijk model is based on six body segments: head, torso, arms, hands, legs, and feet. The Berkeley model (like the Tanabe model) uses sixteen body segments corresponding to the Berkeley segmented thermal manikin (Tanabe, Arens et al. 1994). Each segment in the model is modeled as four body layers (core, muscle, fat, and skin tissues) and a clothing layer. Blood is modeled as a separate series of nodes that provide convective heat transfer between segments and tissue nodes. The model computes heat transfer between each node using a standard finite differencing algorithm with variable time-stepping to optimize computational resources while preserving numerical stability. The treatment of time as a series of discrete “phases” of variable length enables the model to simulate almost any combination of environmental, clothing and metabolic conditions. Effects of transient and spatially asymmetric conditions that are completely lost in whole-body models such as the 2-node PMV model can be predicted by the model. An example simulation might be a person walking from an air-conditioned building to hot summer outdoor conditions and then getting into a car that has been sitting in the sun, turning on the air-conditioning and driving as the car begins to cool off. Applications include evaluating thermal comfort in spaces with asymmetric or transient thermal environments including automobiles, buildings or outdoors. This improved Berkeley Multinode Comfort Model is used as a platform and test bed for the fuzzy control system discussed later. Model Overview The model treats each body part as lumped thermal mass, called node, and simulates the transit thermal response of body by computing the heat transfer between these nodes. The following improvements have been made over the Stolwijk model: • Increase in number of body segments from six to sixteen • Improved blood flow model, including counter flow heat exchange in the limbs • Addition of a clothing node to model both heat and moisture capacitance • Addition of heat loss by conduction to surfaces in contact with the body • Improved convection and radiation heat transfer coefficients • Explicit radiation heat transfer calculation using angle factors • Addition of a radiation heat flux model (e.g. sunlight striking the body) Figure 2 shows a typical segment node structure. This configuration can accommodate most environment conditions and is default implementation. The model, however, is flexible enough and the structure can be modified easily, without recompiling the code, to suit for specific situation. Tfat1 Tmuscle1 Tcore Tskin1 qevap qradiant Tradiant1 Ta Tradiantn Tskin2 Tmuscle2 Tfat2 qconv qconv qevap Tclo Tsurface Tradiantn qradiant Tradiant1 Tskin3 Tmuscle3 Tfat3 Tclo Tcontact Contact surface Tskin4 Tmuscle4 Tfat4 T∞ T∞ Nodes with heat capacity Nodes without heat capacity qevap qevap Figure 2. Typical segment node structure showing four parallel heat paths: top, exposed skin with convective and radiant heat loss; second from top, clothed skin with convection and radiant heat loss; third, clothed skin with conductive loss to contact surface; bottom, bare skin Original Thermoregulation System The lumped node model of human physiology is a passive system which by itself does not exhibit any control, rather, it represents a complex transfer function between regulator and disturbance. The regulating system receives signals from the passive system and exerts corrective effector action on the passive system if there is deviation from preferred conditions. The thermal regulation mechanism used in this model is based on Stolwijk’s original theory with little modification. Finer segmentation resulted in an increased number of signals and corresponding gains. Apart from that, however, the control algorithm remains largely the same. Three types of effector action are, in a qualitative sense, well known. They are sweating, which results in evaporative heat loss, shivering with increased heat production, and vasodilation or vasoconstriction which have the effect of varying skin and muscle blood flow. These action(s) are triggered by error signals -deviations of body parts temperature from their set points. The gains are modeled by a set of coefficients. In modeling the regulator, the following assumptions have been made: 1. Sensors are located in head core, muscle, and evenly distributed in the skin. 2. The signals received from these sensors vary linearly with the local temperature within physiological limits, insensible to the rate of change of local temperature. This is in accord with available experimental observation. 3. Each of these sensor systems has zero output at a local temperature corresponding to a set point. 4. Signal from head core plays a far more important role in determining what the major effector action should take, be it increasing heat loss by sweating and/or vasodilation or increasing heat storage by shivering and/or vasoconstriction. It is not clear what the physical meaning of the set points is. It can be viewed as a kind of thermal neutrality where the regulator has zero output. However, depending upon the physical properties of the body and the environment, these set points may not be the preferred temperatures at which the body tries to stay. In other words, at steady state, body temperatures may be quite different from these set points. This result is not surprising in that, for a linearized system, in order for the steady state to track reference, the closed loop system must have a pole at origin. This may not the case in many situations. The regulator itself is a complex nonlinear system which combines error signals from sensors all over the body and produces control effort. Temperature of each node is compared against its set point. The deviations of all skin nodes are summarized to form one skin signal. It is multiplied by head core signal. A series of complex, nonlinear operation is performed on these signals then and the final controller output is produced in the form of 4 numerical values -SWEAT, DILAT, STRIC and SHIVER which indicate the extent of four effector actions discussed before, i.e., sweating, vasodilation, vasoconstriction, shivering, respectively. The passive system model uses these values to regulate evaporative heat loss, heat production and the amount of blood flown to skin. For details of the thermoregulating mechanism, please refer to Stolwijk and Hardy[ 1]. Fuzzy Controller The purpose of introducing fuzzy algorithm into the human thermoregulating system is to account for the unmodeled human physiology. Our qualitative knowledge of human thermoregulation is still very limited and the human body is greatly simplified in the model. One big challenge for the original crisp control is that it will produce exactly the same results given the same environment conditions. This is, obviously, not the case for a real body. Human body has adaptation ability which the crisp controller does not model. It is hoped that by applying fuzzy algorithm this situation can be improved. Another belief is that it would be presumptuous of us to assume that human body is doing crisp thermal control (The reason human body is being modeled as a crisp system is that this is the best we have at hand.). Our choice of fuzzy logic system may not be the best to attack this problem, or even worse, fuzzy logic system may not be the answer at all! However, at this point, it can, at least, serve as a good starting point. Structure of Fuzzy Model/Control Figure 3 illustrates the configuration of the fuzzy controller used in this model. Figure 3 Configuration of the fuzzy controller Fuzzy Rule Base Fuzzy Inference Engine Fuzzifier Defuzzifier x in U y in V Fuzzifier Although it seems that singleton fuzzifier is widely used, we feel nonsingleton fuzzifier is more suitable in this problem in that we are mapping temperatures to thermal sensations such as COLD, WARM, etc. and we have some intuitively natural membership functions for these fuzzy sets (will be discussed later) that we would like to use. In this model, thermal sensation, σ, is the linguistic input to the fuzzy controller. σ takes on 7 linguistic values: extremely cold(EC), very cold(VC), cold(C), neutral(N), warm(W), very warm(VW) and extremely warm(EW). The controller, after defuzzification, produces four numerical effector actions mentioned before. Internally, the four effector actions are treated as linguistic variables too. Their linguistic values are out put of the fuzzy inference engine. Membership Functions Because of the finer segmentation, each node of the body can have its own set of membership functions for these thermal sensation values which can be best tuned to match each node’s role in thermoregulation. Figure 4 shows a typical membership function set for skin node. Since the head core plays a far more important role in determining control action (Stolwijk and Hardy[1].), it has a far narrower Neutral range as shown in figure 5. Also note that the slopes of all its membership functions are sharper and the centers are closer to its set point. This indicates the node is more sensitive to deviation and has more say in the vote of thermal action. 28 30 32 34 36 38 40 42 0 0.2 0.4 0.6 0.8 1 1.2 EC VC C N W VW EW T(Deg C) Membership Function of Fuzzy Sets for Typical Skin