............(eq. 1)
Abstract
Risk assessment using artificial intelligence techniques can reduce costs and confer agility to the decisions. When knowledge is intricate, fraught with uncertainties or little known about the inter-variable relationships, Fuzzy Expert Systems can be useful at gathering disperse information and accumulating certainty about a fact. Frequently the knowledge of professionals as well as field observations are the main source of information to establish a knowledge base capable of evaluating critical situations. This work presents the technique of Fuzzy Logic used in the Expert System HgEx developed to diagnose mercury bioaccumulation risk from gold mining operations. It is shown how the system accommodates imprecise data input for variables, such as background level as well as how measurements are transformed into linguistic expressions with respective Degrees of Belief to be handle in a heuristic model (neural equations - Weighted Inference Method). Linguistic terms to express risk levels have the same practical effect as complex mathematical models which usually demand high costs, much data and skill to quantify the relationships between each factor and bioaccumulation.
Paper presented at IV Encuentro Hemisferio Sur sobre Tecnologia Mineral, Concepcion, Chile, Nov. 20-23, 1994.
Introduction
Environmental risk assessment has been applied to establish pollution levels in sediment, water and biota as well as to support political and technical decisions to apply remedial procedures. Monitoring programmes are usually used to establish the pollution level. Chemical analysis is clearly as one of the main points to be improved to obtain reliable results for a trustworthy risk assessment. This requires high cost and well trained personnel and still generates reports with vagueness and uncertainties mainly because of sampling uncertainties. Conclusions frequently carry terms such as "more work is needed" or "data are showing preliminary results". For a preliminary approach, the costs involved should be compatible with the results, however this is not frequently observed. In contrast most efforts in environmental research are devoted to search for precision in the analytical analysis together with a reduction of the detection limits of the analytical techniques to parts per trillion level. Will more conclusive reports be generated with sophisticated equipment ? An environmental researcher would probably answer this question with terms such as "maybe" or "likely". Surely the quest for precision in analytical labs is important for certain environmental research, but this is questionable when a preliminary study is being conducted.
Colorimetric kits were suggested as a rapid and efficient way to survey areas for mineral exploration (Veiga et al., 1987) and for enviromental assessment (Veiga and Fernandes, 1990). The development of "in situ" analysis was successfully applied to identifiy "hot spots" (sites with high mercury concentration) in Poconé, MT, Brazil as well to follow the clean-up operations (CETEM, 1989, 1991). In spite of low detection limits and low precision, colorimetric kits by its simplicity and low cost can be useful for a preliminary toxicological evaluation based on hair analysis (Alexandre Pessoa da Silva, CETEM, pers. comm.)
Sampling is another aspect usually ignored in risk assessment reports as a critical point for reliable results. Little information is available in the literature about standard procedures as well as the number of samples required. Large numbers of samples are frequently observed as the normal procedure to obtain reliable results. While this approach improves the quality of the statistical analysis, it does not guarantee that conclusive results are produced.
Statistical approaches have been used to support conclusion (even preliminary) in risk assessment reports. A specific example of the classical approach can be seen in the case of mercury pollution research in Sweden. Swedish researchers have attempted to formulate mathematical models to predict mercury bioaccumulation based on environmental variables measured in lakes. A tendency for increased mercury in fish over the years has been recorded. Correlations between geographical, physical and chemical variables and Hg in fish was established by Håkanson et al (1988) based on very scattered data from 1386 lakes. The data were reduced to 57 lakes to generate an empirical equation which was statistically significant at the 99.5% level with an r2 of 0.78 between predicted and observed Hg levels. But in fact, even with their heuristically-filtered approach, this equation had a error range of about ± 50%!
So application of statistical analysis to masses of data requires significant data reduction that generates empirical results that must be used with extreme caution. Why not apply the heuristics directly to generate logical conclusions which can be explained in terms of a knowledge base search pattern? When an issue has many components and variables with little quantifiable interconnections, the experience of professionals and case studies can help bring together information to establish a standard of behaviour (Pivello, 1991). Heuristic Systems are appropriate tools to deal with situations fraught with vagueness, theory not well established and lack of experts.
The term "heuristics" comes from the Greek word for discovery. Heuristics are decision rules which contain information on problem solving. They may involve designed experimentation or "rules-of-thumb" based on trial-and-error processes. Humanity has learned to deal with complexity by using heuristics (Parkin, 1994).
Finding an optimum solution to complex problems usually involves time and money, but these expenditures do not guarantee that a solution is found. In such situations, satisfactory decisions can be arrived at less expensively by applying heuristics. Heuristics are primarily used for ill-structured problems, but they can also provide reasonable solutions to complex, well-structured problems quicker and cheaper than algorithms (Meech and Kumar, 1993).
The Fuzzy Logic technique devised by Zadeh (1965) employs human analysis to provide an approximate and yet effective means to describe the behaviour of situations which are too complex or too ill-defined to allow precise mathematical analysis. When the knowledge is intricate and little is known about the relationship between variables, Fuzzy Expert Systems are useful to gather disperse information and to accumulate certainty about some facts.
The present work describes the technique of Fuzzy Logic used in an Expert System developed to provide Hg bioaccumulation risk assessment in gold mining regions. HgEx is a heuristic system which accommodates imprecise data input for many variables such as pH, Eh, water conductivity, biomass productivity, water transparency and contaminantion factor. The system does not replace the monitoring programs because all data input are obtained in a field trip, but rather reduces the need for accurate results to provide a preliminary but conclusive risk assessment report. Expert Systems are not a solution to the pollution problem, but rather they can bring additional information to help diagnose dangerous situations and support rapid decisions.
Heuristic System
Heuristic programming involves step-by-step procedures that are executed until a reasonable, satisfactory solution is obtained. The key issue is that the selection of items to test is based on current information. As the current "instance" of the knowledge base is updated, new facts become instantiated, requiring a new selection of sets of rules or other facts to be selected. The process continues until a goal is reached or is proven to be correct (Nilsson, 1980). Heuristic thinking involves searching the problem domain, learning about facts, judging information/decisions, and then repeating this process while solving a problem in a consistent and understandable way.
Although heuristics have served us well, they have also left us with many biased concepts, i.e. we stereotype situations on the basis of little information. In unfamiliar situations, ordinary human beings use heuristics to simplify choice and this may produce bias. However, when experts are performing familiar tasks, these deep processes will be overlain by a patterning that can utilize large blocks of previously learned information to produce split-second judgments (Parkin, 1994). Reverend Bayes almost 200 years ago devised a statistical approach which takes into account a "pre-conceived" judgment about a situation. The essence of this approach rests on the belief that for everything, no matter how unlikely it is, there is a prior probability that it could be true (Savage, 1961). The establishment of the prior probability is empirical (based on previous data) or heuristic (based on experience), which usually involves an expert opinion. Bayesian Statistics was applied in the now-famous Prospector Expert System developed by the Stanford Research Institute, to assess the mineral potential of a site (Duda, et al., 1979).
Expert Systems are computer programs which uses human expertise that is contained within it to make "real world" decisions. This technology advances the capabilities of the computer beyond traditional use, by allowing us to utilize decision-making logic as well as interpreting large amounts of data. In addition to making "smart decisions", these systems are capable of explaining and justifying their behaviour (Meech and Harris, 1990). Conventional Programs execute algorithms and usually deal with quantitative data, Expert Systems uses heuristics and logic and can handle both quantitative and qualitative information.
The Diagnostic part of the HgEx System integrates biological, geochemical, engineering, medical and social data to conclude about emission levels, bioaccumulation risk and the possibility of Hg poisoning through a heuristic model which uses Weighted Inference Equations (basic Neural Equations) to obtain the Degree of Belief in a conclusion (Veiga and Meech, 1994).
The system is able to deal with different types of data input. When available, the user can input measurements obtained in a field trip, which will be converted into linguistic expressions with respective Degree of Belief (DoB) in the concept used by the heuristic model to make new inferences. Lack of analytical measurements can be accommodated in some cases, with questions applied to convert field observations into a DoB through inference equations or rules (Fig. 1).
The structure of HgEx is based on the simple concept that risk of bioaccumulation is a function of the level of mercury emission and the degree of transformation in the environment. Mercury abatement by adsorption on fine ferruginous sediments is the only way in which the risk can decrease. The predicted risk is compared with analyzed biota samples, when available, and conclusions about the current and future bioaccumulation are provided. When the system indicates that there is a high bioaccumulation risk but the biota is not showing high Hg levels, the system suggest frequent monitoring programmes and remedial procedures to avoid future problems.
Fig. 1 - Process in which HgEx deals with data input
Biological samples (fish, snail or human) can provide evidence of bioaccumulation based on chemical results. The Hg concentration in these samples, when available, is input by the user and transformed by Fuzzy Sets into linguistic expressions such as "high", "medium" and "low". These concepts are compared with the bioaccumulation risk predicted by the heuristic model to check for a conflict. If the bioaccumulation evidence is higher than the risk predicted by the system, conflict sources are checked and eventually adaption of the diagnosis is performed.
Linguistic Defuzzification
According to Zadeh (1992), the strength of human reasoning lies in the ability to grasp inexact concepts directly rather than formulating exact ones. Linguistic concepts are characterized by a membership value of each fact in a particular concept. When we characterize a variable in the form of linguistic expressions such as "high", "low", "acidic", "medium", "dark", etc. we have to define the meaning of these expressions. Each expression has a membership grade derived from a discrete value. This grade is called Degree of Belief (DoB). In HgEx, variables when available, such as conductivity, water transparency, Hg concentration, number of gold shops, Eh, pH, etc., are requested from the user to be transformed into expressions with respective DoB to be handled in the heuristic model.
For example, how acidic is pH=5 ? We have built Fuzzy Sets to define the DoB in the concept "acidic". Our belief that pH 5 is acidic is around 80% (Fig. 2). This is less acidic than pH 2 which has a DoB of 99. Fuzzy Sets glide smoothly across a continuum which goes from TRUE to FALSE or DoB = 100 and 0 respectively for each concept. The shape of each fuzzy set is the result of pH-range definitions for soils and sediments (Dragun, 1988) together with the experience of the authors with respect to the domain of this work.
Fig. 2 - Fuzzy Sets to define pH of soils and sediments
If the pH measured in a watercourse is 7.5, then the DoB in "alkaline" is only 30%, and 60% in "neutral" according to Fig. 2. "Very slightly alkaline" would likely be the fuzzy set having full membership at this pH level or 100% DoB. If we narrow the pH range to accomodate more linguistic expressions, we would have a large number of fuzzy sets to describe "precisely" our view point but in this case the linguistic expressions would cope with a semantic problem. How would we describe a fuzzy set in which pH 7.2 would be the member with 100% of DoB ? "Just a little bit alkaline"? "Almost neutral" ? We believe that four fuzzy sets can express reasonably the pH of a sediment.
Each concept has a grade (DoB) that is used in the heuristic model to conclude about the bioaccumulation risk. Weighted Inference Equations can deal with these variables using the importance of each fact (weight) on the conclusion that the environment shows dangerous conditions for methylation and/or bioaccumulation.
Heuristic Model
The heuristic model used in HgEx is adapted from the basic neural equation which propagates weighed evidence to a conclusion. The model is based on the now famous Perceptron network developed by Rosenblatt in 1957 (Minsky and Papert, 1969). All inputs to a node in the network are summed after multiplying by a "suitable" weighting value between 0 and 1.
The Weighted Inference Method derives the DoB in a conclusion multiplying the importance of each evidence (Wi) with the Degree of Belief (DoBi) of the user that the evidence is occurring. This emerges from a single node as a Degree of Belief (DoBconclusion) ranging from 0 to 100 in the concept. The actual output displayed to the user is filtered through a function which involves linguistic defuzzification of the DoBconclusion into terminology which characterizes the spectrum in which the concept ranges (e.g. from non-existent to extremely high). The main advantages of this method are:
Defuzzification to Discrete Value
The heuristic model deals with DoBs in concepts. We have seen above that Fuzzy Sets convert measured variable into DoBs. However, frequently the user may not have analyzed a certain variable. A DoB must be inferred, if this variable is needed. In some cases an exclusive set of questions is displayed to define the variable level. This is the case of water transparency evaluation. The user has to make a choice if the watercourse is "clear", "a bit cloudy", or "muddy" if Secchi disk readings are not available. This exclusive method creates a crisp boundary between each concept, but allows an additional field observation input. With other inputs, Fuzzy Logic can be used to transform qualitative data into inferred numbers in a smoother way as can be seen from our discussion on sediment contamination factor.
Contamination Factor
Sediments are both carriers and sources of contaminants in aquatic systems, i.e they are the best witnesses of a contamination process over the years. The possibility of Hg bioaccumulation is influenced by the contamination level of a sediment. The Index of Geoaccumulation (Igeo) first proposed by G. Müller and described by Förstner et al. (1990) as a quantitative measure of metal pollution in aquatic sediments, uses the relationship between concentration (C) of the element in the sediment (fraction <2 µm) and the background in fossil argillaceous sediment (B):
............(eq. 1)
Rodrigues (1994) applied this index to evaluate the -200 mesh fraction of sediments from "garimpo" areas in Poconé and Alta Floresta and used the Hg concentration of the -200 mesh fraction of non-impacted creek sediments as the background level. Most sediments in Poconé showed Igeo between 0 and 2. An average index of 5 was observed in turbid rivers of Alta Floresta which mirrors the capacity of the fine (ferruginous) sediment to transport adsorbed Hg.
Håkanson (1980) introduced the concept of risk in the sediment analysis. He proposed an "ecological risk index" which takes into consideration a contamination factor, the toxicity of the metal, its abundance, etc. This is a complex index to calculate, but the contamination factor (Cf) is calculated by dividing the mean content of Hg from at least 5 samples by the pre-industrial reference value (0.25 ppm for Hg). This pre-industrial factor was calculated based on an average Hg content in sediments mostly from Swedish lakes. It seems that this factor could be replaced with the background level to be applied in other regions. The process of describing the contamination factor in linguistic terms is the most attractive point of his work (Table 1). Classification of contamination level is a fuzzy concept since the contamination factor is in a continuum gradient derived from comparison between background levels and Hg concentration in sediments.
Table 1 - Description of the Contamination Factor (Cf)
In the HgEx System the Hg concentration in a sediment (-200 mesh fraction), when available, is divided by the background level (analyzed or inferred) to determine the contamination factor and this variable is mapped in Fuzzy sets to obtain the Degree of Belief (DoB) in each of the following linguistic terms : "low", "moderate", "considerable" and "very high" (Fig. 3).
Fig. 3 - Fuzzy Sets to Define the Contamination Factor
When the contamination factor is 1.2, there is 70% of belief in the concept "low" and 30% in "moderate". These terms are taken into account in the heuristic model described above.
Background levels
Mercury is geochemically classified as a chalcophile element (mostly associated with sulphide phases). Jonasson and Boyle (1979) showed a wide range of Hg concentration in igneous rocks but the average is 0.028 ppm for basic and 0.062 ppm for acid rocks. The same authors showed a wide range of Hg concentration in sediments ranging from 0.010 to 3 ppm. A mean of 0.080 ppm of mercury is reported by Taylor (1964) as the earth's crust background.
In the Amazon, the surface material can be influenced by two effects: a) anthropogenic mercury deposited from local or regional sources; b) lithogenic mercury transported from deep to top layers as the water flows toward surface during the dry season. In any case, as suggested by Lindqvist et al. (1991), it seems that the best material to sample for background determination is from B horizon or deeper where the influence of anthropogenic emissions is slight.
In lateritic soils and bottom sediments from Poconé and Alta Floresta ("garimpo" regions), values ranging from 0.1 to 0.3 ppm Hg are accepted as background levels for the -200 mesh (<0.074 mm) fraction (CETEM, 1989, 1991). Lacerda et al. (1990)have analyzed bottom sediments of non-impacted Amazonian river. They found values ranging from 0.05 to 1.2 ppm of Hg for size fractions <0.063 mm. The higher values are related to organic-rich sediments, whereas intermediate numbers were observed for sediments rich in hydrous ferric oxides (HFO).
A field survey to establish background levels is not an easy task. The HgEx system was designed to infer the background level based on sediment colour and mineralogical characteristics. A process of defuzzification provides a inferred background level for use in the contamination factor calculation. This approach can be applied to any environmental monitoring program by adapting the respective variables and fuzzy sets.
The presence of organic matter promotes higher Hg levels in sediments. Grain size can also influence Hg content. Fine fractions concentrate Hg more than coarse ones. Gravels represent coarse sediments composed of limestone, sandstone, or any igneous or metamorphic rocks (e.g. granite, gneiss, diorite, gabbro, etc.) which are rocks usually with low Hg content. The colour of the sediment can also be used to infer Hg background. White sediments are frequently related with parent rocks poor in Hg. The presence of HFO (yellow-red) as a product of weathered mafic minerals or the presence of organic matter (grey-black) will change the Hg background. As these components are strong adsorbents of minute amounts of mercury from waters, their presence in sediments enhances Hg background.
Despite the large diversity of sediment types, when considered with respect to mercury content alone, we can formulate three types which commonly have low, medium and high mercury respectively:
Rules can be built to correlate user belief in a sediment type with a conclusion about Hg level. One rule could be:
IF sediment is classified as Type 1 DoB = 80 (user input) THEN Hg level is low CF = 100
If we consider that the DoBlow = DoBtype 1 * CF/100, the DoB of this conclusion is 80%. The significance of 80% DoBlow can be transformed (or defuzzified) into a discrete value. According to the fuzzy sets established from detailed literature review, we can say from this value that this sediment should have a value around 0.06 ppm Hg, as obtained from the fuzzy set shown in Fig. 4. This is a rather low value for even Type 1 sediments. Most have contents above 0.07 ppm although values as low as 0.003 have been infrequently measured. So with this uncertainty, we would prefer to have a much higher Hg level chosen. As will be seen, an exponential Inferencing Equation can be used to achieve this performance.
Fig.4 - Fuzzy Sets for "low, medium and high" Hg Levels in Sediments.
As well when other components with high mercury concentration are present in the sediment, but the user still believes that Type 1 best describes the case, the rule becomes more complex:
IF sediment is classified as Type 1 DoB = 80 (User input) AND hydrous ferric oxides are present DoB = 100 AND sulphide mineral is present DoB = 100 AND organic matter is present DoB = 100 THEN Hg level is low CF = 0
In this case, the Certainty Factor is zero, i.e. the user may believe that this sediment is better classified as Type 1, but the system will not believe in a low Hg level since the presence of other components most certainly increases the natural Hg concentration. Regardless of the method used to combine the DoBs of the premises, we know that the Degree of Belief of this conclusion (low Hg level) is zero provided the DoBs of all premise parts exceed the confidence level. Otherwise the firing of this rule will be unsuccessful.
So, the DoB of the conclusion must accommodate cases between False and True. An Inference Equation can play this role, i.e. an equation established to correlate DoBtype 1 and DoBlow together with the DoB values associated with Hg-containing minerals. Sometimes, a synergetic effect between premises is desired. An empirical equation has been derived from the two extremes cases shown above that is capable of accumulating all ranges of belief in the various sediment species:
...........(eq.2)
where: DoBFe oxide , DoBsulphides and DoBorganics are the degrees of belief input by the user about the presence of each of these sediment components.
Equation 2 is the mathematical result of heuristic reasoning which correlates Hg levels with sediment components as shown in Fig. 5. The desired exponential decay relationship between DoBtype 1 and DoBlow is apparent. Only a single rule is necessary to obtain this relationship.
Equations to relate Type 2 and Type 3 with the concepts of medium and high Hg levels, respectively, were also heuristically developed :
...........(eq. 3)
...........(eq. 4)
The DoBorganics is obtained by a colour scale from white to black or from 0 (false) to 100 (true). When the user selects a tint of grey, the system takes the associated DoBorganics with the colour.
Fig. 5 - Relationship between degrees of belief in low and sediment type.
Subsequent defuzzification obtains a discrete value from the respective Fuzzy Sets (Fig. 4). Defuzzification can follow one of 80 different reasoning methods, any of which under different circumstances can provide the "best" result. For the purposes of this work, it was decided to use an adaptation of the Weighted Average Method (eq. 5) combining the DoB in each concept: low, medium and high.
...........(eq. 5)
where :
B = inferred background (ppm)
DoBi = Degree of Belief in low, medium or high
Hgi = Hg (ppm) extracted from each Fuzzy Set
n = number of linguistic sets
This technique is useful to provide the user with an analysis even when the background level was not established in a field survey. In this way, the contamination factor can be inferred from direct observations about the sediment.
A reasonable definition of pollutant is "a substance present in greater than natural concentration as a result of human activity and having a net detrimental effect upon its environment or upon something of value in that environment". Contaminants, which are not classified as pollutants unless they have some detrimental effect, cause deviation from the normal composition of an environment (Manahan, 1991). Since pollution implies a toxic situation, the contamination factor is not sufficient to characterize bioaccumulation risk. Mercury Bioaccumulation has been studied for almost three decades by researchers all over the world. The knowledge accumulated in this field still has many uncertainties and a number of controversies about the effect of some variables have been raised (Richman et al., 1988; Verta et al., 1986, D'Itri, 1990) but the influence on bioaccumulation of pH, humosity, conductivity, biomass, solids in suspension and Hg in sediments seems to be applicable to most environments. So, the system takes into account all these variables in the heuristic model to conclude about environmental risk for biota and humans.
Conclusions
Expert Systems can play an important role in transferring heuristic knowledge to non-technical people who need a rapid and efficient risk assessment report. Risk assessment using artificial intelligence techniques can reduce costs and confer agility to the decisions. Heavy metal pollution has a major impact on the bioaccumulation processes. These mechanisms are usually complex. Since the subject is fraught with uncertainties about the effects of natural variables, the knowledge base must accommodate imprecise data input based on field observations. Fuzzy Logic and Weighted Inference Equations are suitable techniques to deal with heuristic knowledge to mimic Expert reasoning, conferring elasticity to the Degree of Belief calculated for conclusions. In this particular case, linguistic terms have the same practical effect as complex mathematical models which usually demand high costs, much data and skill to quantify the relationships between each factor and bioaccumulation. Rapid diagnosis can bring rapid decisions. Even preliminary decisions are useful to help remedy pollution hazards.
References
Manahan, S.E., 1991. Environment Chemistry. 5th ed. Chelsea, Michigan, Lewis Publishers. 583p.
Minsky, M. and Papert, S.1969. Perceptrons. MIT Press, Cambridge, MA, USA.
Nilsson, 1980 - Principles of Artificial Intelligence, Tioga Press, Palo Alto, CA, USA
Pivello, V. R., 1991. Sistemas Especialistas no Manejo Ambiental. Ambiente, v.5, n.1, p.52-57
Zadeh, L.A., 1965. Fuzzy Sets. Information and Control, v.8, p.338-353.
Zadeh, L.A., 1992 - The Calculus of Fuzzy If/Then Rules. AI Expert, March 1992, p.23-27
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