Results of FNN TSK forecasting.
\r\n\t• Role of technological innovation and corporate risk management
\r\n\t• Challenges for corporate governance while launching corporate environmental management among emerging economies
\r\n\t• Demonstrating the relationship between environmental risk management and sustainable management
\r\n\t• Contemplating strategic corporate environmental responsibility under the influence of cultural barriers
\r\n\t• Risk management in different countries – the international management dimension
\r\n\t• Global Standardization vs local adaptation of corporate environmental risk management in multinational corporations.
\r\n\t• Is there a transnational approach to environmental risk management?
\r\n\t• Approaches towards Risk management strategies in the short-term and long-term.
The problems of banks financial state analysis and bankruptcy risk forecasting are of great importance. The opportune discovery of coming bankruptcy allows top bank managers to make urgent decisions for preventing the bankruptcy. Nowadays, there are a lot of methods and techniques of banks state analysis and determination of bank rating—WEB Money, CAMEL [1], Moody’s S&P, etc. But their common drawback is that all of them work with complete and reliable data and cannot give correct results in case of incomplete and unreliable input data. This is especially actual for the Ukrainian banking system where bank managers often provide the incorrect reports about bank financial state to obtain new credits and loans.
\nTherefore, it is very important to create new methods for banks bankruptcy risk forecasting under uncertainty. The main goal of present investigation is to consider and estimate novel methods of bank financial state analysis and bankruptcy risk forecasting under uncertainty and compare with classical methods. The implementation and assessment of the efficiency of the suggested methods are performed at the problems of bankruptcy risk forecasting for Ukrainian and European banks.
\nAs it is well known, the year 2008 was the crucial year for the bank system of Ukraine. If the first three quarters were periods of fast growth and expansion, the last quarter became the period of collapse in the financial sphere. A lot of Ukrainian banks faced the danger of coming default.
\nFor this research, the quarterly accountancy bank reports used were obtained from National bank of Ukraine site. For analysis, the financial indices of 170 Ukrainian banks were taken up to the date January 01, 2008 and July 01, 2009, that is, about two years before crises and just before the start of crises [2].
\nThe important problem that occurred before the start of the investigations is which financial indices are to be used for better forecasting of possible bankruptcy. Thus, another goal of this exploration was to detect the most relevant financial indicators for obtaining maximal accuracy of forecasting.
\nFor analysis, the following indicators of banks accountancy were considered:
assets, capital, financial means, and their equivalents; and
physical person’s entities, juridical person’s entities, liabilities, and net incomes (losses).
The collected indicators were used for analysis by fuzzy neural networks as well as classic statistical methods. As output data of models for Ukrainian banks were two values:
1, if the significant worsening of bank financial state is not expected in the nearest future
−1, if the bank bankruptcy is expected in the nearest future.
For forecasting of banks bankruptcy risk, the application of fuzzy neural networks (FNN) ANFIS and TSK was suggested [3]. The application of FNN is determined by following reasons:
the capability to work with incomplete and unreliable information under uncertainty; and
the capability to use expert information in the form of fuzzy inference rules.
Let us consider the mathematical model and training algorithm of a fuzzy neural network TSK (Takagi, Sugeno, Kang’a), which is generalization of the neural network ANFIS. The rule base of FNN TSK with M rules and N variables can be written as follows [3]:
where \n
At the intersection of the TSK network rule conditions, \n
With M inference rules, the general output of FNN TSK is determined by the following formula:
\nwhere \n
The fuzzy neural network TSK, which implements the output in accordance with (3), represents a multilayer network whose structure is shown in Figure 1.
\nThe structure of TSK fuzzy neural network.
This network has five layers with the following functions:
The first layer performs fuzzification separately for each variable \n
The second layer performs the aggregation of individual variables \n
The third layer is a function generator TSK, wherein the output values are calculated \n
The fourth layer consists of two summing neurons, one of which calculates the weighted sum of the signals \n
The fifth layer is composed of a single output neuron. In it, weight normalizing is performed and the output signal determined in accordance with the expression:
This is also nonparametric layer.
\nFrom this description follows that TSK fuzzy network contains only two parametric layers: first and third, the parameters of which are determined in the training process. Parameters of the first layer \n
If we assume that at any given time moment, the nonlinear parameters are fixed, then the function \n
In the presence of N input variables, each rule \n
Considering a hybrid learning algorithm which is used for FNN TSK, all parameters can be divided into two groups. The first group includes linear parameters \n
In the first stage after fixing the individual parameters of the membership function by solving a system of linear equations, linear parameters of polynomial \n
where
\nWith the dimension L of training sample \n
where \n
Matrix \n
where \n
In the second stage, after fixing the values of linear parameters \n
Then, the error vector \n
The error signals are sent through the network backward according to the method of back propagation until the first layer, at which gradient vector components of the objective function with respect to parameters \n
After calculating the gradient vector, a step of gradient descent method is made. The corresponding formulas (for the simplest method of the steepest descent) are the following:
\nwhere n is a number of iterations.
\nAfter verifying the nonlinear parameters, the process of adaptation of linear parameters TSK (first phase) restarts and nonlinear parameters are further adapted (second stage). This cycle continues until all the parameters will be stabilized.
\nFormulas (11)–(13) require the calculation of the gradient of the objective function with respect to the parameters of the MF. The final form of these formulas depends on the type of MF. For example, if using the generalized bell-wise functions:
\nthe corresponding formulas for gradient of the objective function for one pair of data \n
In the practice of the hybrid learning method implementation, the dominant factor in adaptation is considered to be the first stage in which weights \n
It is worth to note that the described hybrid algorithm is one of the most effective ways of training fuzzy neural networks. Its principal feature is the division of the process into two stages separated in time. Since the computational complexity of each nonlinear optimization algorithm depends nonlinearly on the number of parameters subject to optimization, the reduction in the dimensions of optimization significantly reduces the total amount of calculations and increases the speed of convergence of the algorithm. Due to this, hybrid algorithm is one of the most efficient in comparison with conventional gradient-based methods.
\nA special software kit was developed for FNN ANFIS and TSK application in bankruptcy risk forecasting problems. As input data, the financial indicators of Ukrainian banks in financial accountant reports were used in the period of 2008–2009 [2] . As the output values were used +1, for bank nonbankrupt and −1, for bank bankrupt. In the investigations, various financial indicators were analyzed, and different number of rules for FNN and the analysis of data collection period influence on forecasting accuracy were performed.
\nThe results of experimental investigations of FNN application for bankruptcy risk forecasting are presented below.
\nIn the first series of experiments, input data at the period of January 2008 were used (that is for two years before possible bankruptcy) and possible banks bankruptcy was forecasted at the beginning of 2010.
\n\n
Training sample—120 Ukrainian banks, test sample—50 banks.
Number of rules = 5.
Input data—financial indices (taken from bank accountant reports):
assets, capital, cash (liquid assets), households deposits, liabilities.
The results of application of FNN TSK are presented in Table 1.
The similar experiments were carried out with FNN ANFIS.
The goal of the next experiment was to find out the dependence of rule number on predicting accuracy. Input data—the same financial indices as in experiment 1.
\nThe results of application of FNN TSK are presented in Table 2.
\nThe similar experiments were carried out with FNN ANFIS.
\nThe comparative analysis of forecasting results versus the number of rules is presented in Table 3 [4].
\nComparing the results in Table 3, one may conclude FNN TSK has better accuracy than FNN ANFIS.
\nThe goal of the next experiments was to explore the influence of training and test samples size on accuracy of forecasting.
\n\n
Training sample—120 Ukrainian banks, test sample—50 banks, and number of rules = 10.
Input data—financial indicators:
assets, entity, cash (liquid assets), household deposits, and liabilities.
The results for FNN TSK are presented in Table 4.
\nThe similar experiments were carried out with FNN ANFIS.
\nAfter analysis of the experimental results the following conclusions were made:
FNN TSK ensures the higher accuracy of risk forecasting than FNN ANFIS;
the variation of the number of rules in the training and test samples makes slight influence on the accuracy of forecasting; and
the goal of the next series of experiments was to determine the optimal input data (financial indicators) for bankruptcy risk forecasting. The period of input data was January 2008.
\n
Number of banks and rules were the same as in previous experiment 4.
Input data—financial indicators (taken from banks financial accountant reports):
profit of current year, net percentage income, net commission income; and
net expense on reserves and net bank profit/losses.
The results of FNN TSK application are presented in Table 5.
\n\n
Number of banks and rules were the same as in the previous experiment 5.
Input data—the financial indicators (taken from banks financial accountant reports):
general reliability factor (own capital/assets);
instant liquidity factor (liquid assets/liabilities);
cross coefficient (total liabilities/working assets);
general liquidity coefficient (liquid assets + defended capital + capitals in reserve fund/total liabilities); and
coefficient of profit fund capitalization (own capital/charter fund).
The results for FNN TSK are presented in Table 6.
\nIt is worth to note that these financial indicators are also used as input data in Kromonov’s method of banks bankruptcy [5, 6, 7], whose results are presented below.
\n\n
Training sample—120 Ukrainian banks and test sample—70 banks.
Number of rules = 5.
Input data—following financial indicators (other than in experiments 5 and 6):
ROE—return on entity (financial results/entity);
ROA—return on assets (financial results/assets);
CIN—incomes-expenses ratio (income/expense);
NIM—net percentage margin; and
NI—net income.
The results of application of FNN TSK for forecasting with these input indicators are presented in Table 7.
\nIt should be noted that these indicators are used as input in the method of Euro Money [1].
\n\n
Training sample—120 Ukrainian banks and test sample—70 banks.
Number of rules = 5.
Input data—financial indicators (banks financial accountant reports):
general reliability factor (own capital/assets);
instant liquidity factor (liquid assets/liabilities);
cross coefficient (total liabilities/working assets);
general liquidity coefficient (liquid assets + defended capital + capitals in reserve fund/total liabilities);
coefficient of profit fund capitalization (own capital/charter fund); and
coefficient entity security (secured entity/own entity).
The results of FNN TSK application with these financial indicators are presented in Table 8.
\nThe comparative analysis of forecasting results using different sets of financial indicators are presented in Table 9.
\n\nNext experiment was aimed on finding the influence of data collection period on the forecasting results. It was suggested to consider two periods: January of 2008 (about 1.5 year before the crisis) and July of 2009 (just before the start of crisis).
\n\n
Training sample—120 Ukrainian banks and test sample—70 banks.
Number of rules = 10.
Input data—financial indices, the same as in experiment 8.
In Table 10, the comparative results of forecasting versus period of input data are presented.
\nResults | \n|
---|---|
Total amount of errors | \n5 | \n
% of errors | \n10 | \n
First type of errors | \n0 | \n
Second type of errors | \n5 | \n
Results of FNN TSK forecasting.
Results | \n|
---|---|
Total amount of errors | \n6 | \n
% of errors | \n12 | \n
First type of errors | \n1 | \n
Second type of errors | \n5 | \n
Results of FNN TSK forecasting.
Network/number of rules | \nTotal number of errors | \n% of errors | \nNumber of first type errors | \nNumber of second type errors | \n
---|---|---|---|---|
ANFIS 5 | \n6 | \n12 | \n0 | \n6 | \n
ANFIS 10 | \n7 | \n14 | \n1 | \n6 | \n
TSK 5 | \n5 | \n10 | \n0 | \n5 | \n
TSK 10 | \n6 | \n12 | \n1 | \n5 | \n
Comparative analysis of FNN ANFIS and TSK in dependence on rules number.
Results | \n|
---|---|
Total number of errors | \n7 | \n
% of errors | \n10 | \n
First type of errors | \n1 | \n
Second type of errors | \n6 | \n
Results of FNN TSK forecasting.
Results | \n|
---|---|
Total number of errors | \n13 | \n
% of errors | \n19 | \n
First type of errors | \n6 | \n
Second type of errors | \n7 | \n
Results of FNN TSK forecasting.
Results | \n|
---|---|
Total number of errors | \n7 | \n
% of errors | \n10 | \n
First type of errors | \n1 | \n
Second type of errors | \n6 | \n
Results of FNN TSK forecasting.
Results: | \n|
---|---|
Total number of errors | \n12 | \n
% of errors | \n17 | \n
First type of errors | \n5 | \n
Second type of errors | \n7 | \n
Results of FNN TSK forecasting.
Results | \n|
---|---|
Total amount of errors | \n8 | \n
% of errors | \n13 | \n
First type of errors | \n1 | \n
Second type of errors | \n7 | \n
Results of FNN TSK forecasting.
Experiment | \nTotal number of errors | \n% of errors | \nFirst type of errors | \nSecond type of errors | \n
---|---|---|---|---|
Experiment 5 | \n13 | \n19 | \n6 | \n7 | \n
Experiment 6 | \n7 | \n10 | \n1 | \n6 | \n
Experiment 7 | \n12 | \n17 | \n5 | \n7 | \n
Experiment 8 | \n8 | \n13 | \n1 | \n7 | \n
The dependence of forecasting accuracy on sets of input financial indices.
Experiment/number rules | \nTotal number of errors | \nFirst type of errors | \nSecond type of errors | \nTotal % of errors | \n
---|---|---|---|---|
January 1, 2008 5 rules | \n7 | \n0 | \n7 | \n10 | \n
July 1, 2009 5 rules | \n5 | \n0 | \n5 | \n7 | \n
July 1, 2009 10 rules | \n7 | \n3 | \n4 | \n10 | \n
Accuracy of forecasting in dependence on data collection period.
In the process of investigations, fuzzy group method of data handling (FGMDH) was also suggested for financial state of Ukrainian banks forecasting [3]. GMDH is the inductive modeling method that enables to construct a model automatically by experimental data [3]. As input data, the same indices were used as in the experiments with FNN TSK.
\nIn Table 11, the forecasting accuracy of FGMDH is presented in dependence on input data collection period.
\nInput data period | \nTotal error number | \n% of errors | \nFirst type of errors | \nSecond type of errors | \n
---|---|---|---|---|
2004 | \n10 | \n14 | \n3 | \n7 | \n
2005 | \n9 | \n13 | \n3 | \n6 | \n
2006 | \n8 | \n11.4 | \n3 | \n5 | \n
2007 | \n7 | \n10 | \n2 | \n5 | \n
2008 | \n6 | \n8.5 | \n1 | \n5 | \n
2009 | \n6 | \n8.5 | \n2 | \n4 | \n
Comparative results of forecasting using method FGMDH in dependence on period of input data collection.
If we compare the results of FGMDH with the results of FNN TSK, one can see that FNN TSK gives better results for short-term risk forecasting (one year before possible bankruptcy) while FGMDH has better accuracy using older input data and so it has advantages in long-term forecasting (2 or more years).
\nIn the concluding experiments, the comparative analysis of application of all the considered methods was carried out. The following methods were considered [4]:
fuzzy neural network ANFIS;
fuzzy neural network TSK; and
crisp forecasting methods: Kromonov’s method and Byelorussian bank association method.
As input data, the financial indices of Ukrainian banks on July 2007 year were used. The results of application of all methods for bankruptcy risk analysis are presented in Table 12.
\nMethod/period | \nTotal amount of errors | \n% of errors | \nFirst type of errors | \nSecond type of errors | \n
---|---|---|---|---|
ANFIS | \n7 | \n10 | \n1 | \n6 | \n
TSK | \n5 | \n7 | \n0 | \n5 | \n
GMDH | \n6 | \n8.5 | \n1 | \n5 | \n
Kromonov’s method | \n10 | \n15 | \n5 | \n5 | \n
BBA method | \n10 | \n15 | \n2 | \n8 | \n
Comparative results analysis of various forecasting methods.
The most widely used approach of banks financial state analysis and bankruptcy risk forecasting is based on the application of rating systems. The determination of bank rating is one of the methods that enables to obtain complex financial assessment of bank financial state and compare them. There are various private and official banks rating systems. The most known of them are systems developed by world leaders in this sphere-rating companies Fitch, Standard & Poor’s, Moody’s, etc. Officially recognized banks rating system that is widely used in the world is system CAMELS. It’s American rating system was developed and implemented by Federal reserve System (FRS) and Federal Deposit Insurance Corporation (FDIC) in 1978 [1].
\nSupervision over banks activity based on risk estimation by system CAMELS lies in determination of general bank state using the common criteria that defines all aspects and spheres of bank activity. This system is also widely used in Ukraine by National Bank of Ukraine (NBU) according to developed “Statement of order of rating estimates determination by rating system ‘CAMELS’.”
\nRating system CAMELS allows NBU to estimate general financial state and stability of banking system of Ukraine. Such assessment enables to obtain information for priority determination in banking supervision activity and necessary materials and financial resources for performing adequate control over banking system.
\nAt the same time, system CAMELS envisages the detail supervision and analysis of bank state. Such analysis may be performed only while complex inspecting checking of bank activity, which enables to determine how the top managers analyze and control bank risks.
\nThe base of rating system, CAMELS, is risk assessment and determination of rating estimates by each component of the system: capital adequacy, assets quality, management, liquidity, and sensitivity.
\nDue to rating system, each bank obtain digital rating by all six components, and integral (complex) rating estimate is determined on the base of rating estimates of all components. Components of rating system are estimated by 5 balls scale in which estimate 1 is the highest, and estimate 5 is the lowest one. Integral estimate is also determined by 5 balls scale. Banks that obtained integral rating estimate 1 or 2 are considered reliable by all the factors capable to overcome economic depression and its management believed to be qualified.
\nBanks that got integral estimate 3 have substantial drawbacks, which may lead to serious problems with liquidity and solvency if these drawbacks won’t be corrected in proper time. In this case, bank’s supervision system should give recommendations to managers how to overcome existing problems.
\nBanks that got rating estimate 4 or 5 have serious problems, which demand strict supervision and special urgent actions to prevent possible bankruptcy (see Table 13).
\nFor bankruptcy risk forecasting in banking sphere of Ukraine, a special data set was collected consisting of 160 Ukrainian banks in the period 2012–2014 . It was divided into training and test subsamples in ratio 70/30 for FNN TSK, i.e., training samples consisted of 110 banks and test samples of 50 banks. The experiments were carried out, and the following results were obtained for FNN TSK (in average, 20 experiments were performed for each year and rules number), which are presented in Table 2. The data were collected in the year indicated in the first column, and the forecasting was made for next year, e.g., 2012-5—means bankruptcy risk forecasting in 2013 with use of 5 rules in FNN TSK by data of 2012. Two types of experiments were carried out with fixed parameters of membership functions (MF) and with training MF parameters. In Table 14, forecasting results for FNN TSK with adaptation of parameters are presented and in Table 15 with fixed parameters values.
\n\n | Bank integral rating | \n||||
---|---|---|---|---|---|
“1” | \n“2” | \n“3” | \n“4” | \n“5” | \n|
Bank financial state | \nBank is stable, reliable, and has skilled management | \nBank has substantial drawbacks, which may lead to serious problems in future. | \nBank faces very serious problems, which may lead to bankruptcy. | \n||
Control from banks supervision service | \n\n | Bank supervision service should give clear instructions to overcome existing problems. | \nBanks need urgent actions to prevent possible bankruptcy. | \n||
Application of special actions | \n\n | Proper influence actions are performed over bank due to demands of existing regulation laws of NBU. | \n
Comparative results analysis of various forecasting methods.
Year and number of rules | \nGeneral number of errors | \n% of errors | \nNumber of first type errors | \nNumber of second type errors | \n
---|---|---|---|---|
2012—5 | \n6 | \n12 | \n0 | \n6 | \n
2013—5 | \n9 | \n18 | \n0 | \n9 | \n
2014—5 | \n8 | \n16 | \n1 | \n7 | \n
2012—10 | \n7 | \n14 | \n2 | \n5 | \n
2013—10 | \n5 | \n10 | \n0 | \n5 | \n
2014—10 | \n10 | \n20 | \n4 | \n6 | \n
Forecasting results for FNN TSK with FM parameters’ adaptation.
Year and number of rules | \nGeneral number of errors | \n% of errors | \nNumber of first type errors | \nNumber of second type errors | \n
---|---|---|---|---|
2012—5 | \n8 | \n16 | \n1 | \n7 | \n
2013—5 | \n8 | \n16 | \n0 | \n8 | \n
2014—5 | \n9 | \n18 | \n1 | \n8 | \n
2012—10 | \n9 | \n18 | \n3 | \n6 | \n
2013—10 | \n7 | \n14 | \n1 | \n6 | \n
2014—10 | \n11 | \n22 | \n4 | \n7 | \n
Forecasting results for FNN TSK with fixed parameters.
In Table 16, forecasting results for FNN TSK with triangular MF are presented, while in Table 17 with trapezoidal MF.
\nYear and number of rules | \nGeneral number of errors | \n% of errors | \nNumber of first type errors | \nNumber of second type errors | \n
---|---|---|---|---|
2012—5 | \n9 | \n18 | \n1 | \n8 | \n
2013—5 | \n7 | \n14 | \n1 | \n6 | \n
2014—5 | \n9 | \n18 | \n0 | \n9 | \n
2012—10 | \n11 | \n22 | \n4 | \n7 | \n
2013—10 | \n10 | \n18 | \n2 | \n8 | \n
2014—10 | \n13 | \n26 | \n4 | \n9 | \n
Forecasting results for FNN TSK with triangular MF.
Year and number of rules | \nGeneral number of errors | \n% of errors | \nNumber of first type errors | \nNumber of second type errors | \n
---|---|---|---|---|
2012—5 | \n7 | \n14 | \n1 | \n8 | \n
2013—5 | \n8 | \n16 | \n1 | \n6 | \n
2014—5 | \n5 | \n10 | \n0 | \n9 | \n
2012—10 | \n9 | \n18 | \n4 | \n7 | \n
2013—10 | \n12 | \n24 | \n2 | \n8 | \n
2014—10 | \n11 | \n22 | \n4 | \n9 | \n
Forecasting results for FNN TSK with trapezoidal MF.
The application of well-known matrix method by Nedosekin [11, 12] with level (threshold) of cut 0.7 gave the following results presented in Table 18.
\nYear and number of rules | \nGeneral number of errors | \n% of errors | \nNumber of first type errors | \nNumber of second type errors | \n
---|---|---|---|---|
2012—0,7 | \n14 | \n28 | \n8 | \n6 | \n
2013—0,7 | \n11 | \n22 | \n3 | \n8 | \n
2014—0,7 | \n16 | \n32 | \n9 | \n7 | \n
Forecasting results of matrix method by Nedosekin.
Results obtained by rating system CAMEL are presented in Table 19 (threshold of 4).
\nYear and number of rules | \nGeneral number of errors | \n% of errors | \nNumber of first type errors | \nNumber of second type errors | \n
---|---|---|---|---|
2012—4 | \n12 | \n24 | \n7 | \n5 | \n
2013—4 | \n14 | \n28 | \n5 | \n9 | \n
2014—4 | \n9 | \n18 | \n5 | \n4 | \n
Forecasting results of rating system CAMEL.
In Figure 2, the probability of error for different forecasting methods and various MF is presented.
\nBankruptcy risk forecasting results for different methods.
In Figure 3, dependence of error probability versus number of rules in FNN TSK is presented.
\nError probability for different rules number in FNN.
Analyzing the performed experiments, the following conclusions may be made.
The experimental investigations of efficiency of different forecasting methods FNN TSK, matrix method of Nedosekin, and rating system CAMELS were carried out for the problem of bankruptcy risk forecasting of Ukrainian banks.
Results obtained by FNN TSK are the best (min error%). Mean forecasting accuracy by TSK with Gaussian MF is equal to 85%, with trapezoidal MF mean accuracy is 82%, triangular MF gives 79%, matrix method of Nedosekin −70%, while standard rating system CAMELS has 75% accuracy.
With the increase of rules, number error probability first decreases, then attains minimum and then begins to raise.
Various methods for Ukrainian banks financial state forecasting were considered and analyzed. The following methods were considered [3, 4]: fuzzy neural network ANFIS, fuzzy neural network TSK, Kromonov’s method, Byelorussian bank association method, rating system CAMELS, and matrix method (Nedosekin).
\nAs the input data, the financial indices of Ukrainian banks were considered.
\nWhile experiments with the adequate financial indicators were detected using which the best forecasting results for Ukrainian banks were obtained:
general reliability factor (own capital/assets);
instant liquidity factor (liquid assets/liabilities);
cross coefficient (total liabilities/working assets);
general liquidity coefficient (liquid assets + defended capital + capitals in reserve fund/total liabilities); and
coefficient of profit fund capitalization.
It was established that FNN TSK gives much more accurate results than FNN ANFIS. With increase of rules, number error probability first decreases, then attains minimum and then begins to raise.
The fuzzy GMDH gives better results using older data that is, more preferable for long-term forecasting (two or more years).
The comparison of FNN TSK with standard rating system CAMELS has shown that TSK enables to obtain more accurate bankruptcy risk forecasting.
In general, the comparative analysis had shown that fuzzy forecasting methods and techniques give better results than the conventional crisp and rating methods for forecasting bankruptcy risk. But at the same time, the crisp methods are more simple in implementation and demand less time for their adjustment.
The results of successful application of fuzzy methods for bankruptcy risk forecasting of Ukrainian banks under uncertainty stimulated the further investigations of these methods application for financial state analysis of European leading banks.
\nThe main goal of this exploration was to investigate novel methods of European banks bankruptcy risk forecasting, which may work under uncertainty with incomplete and unreliable data.
\nBesides, the other goal of this investigation was to determine which factors (indicators) are to be used in forecasting models to obtain results close to real data. Therefore, we used a set of financial indicators (factors) of European banks according to the International accountant standard IFRS. The annual financial indicators of about 300 European banks were collected in 2004–2008, preceding the start of crisis of bank system in Europe in 2009. The data source is the information system Bloomberg [8]. The resulting sample included the reports only from the largest European banks as system Bloomberg contains the financial reports only from such banks. For correct utilization, input data were normalized in interval [0,1].
\nThe period for which the data were collected was 2004–2008. The possible bankruptcy was analyzed in 2009. The indicators of 165 banks were considered among which more than 20 banks displayed the worsening of the financial state in that year. Fuzzy neural networks and Fuzzy Group Method of Data Handling (FGMDH) were used for bank financial state forecasting.
\nIn accordance with the above stated goal, the investigations were carried out for detecting the most informative indicators (factors) for financial state analysis and bankruptcy forecasting. Taking into account incompleteness and unreliability of input data, FNN ANFIS and TSK were suggested for bankruptcy risk forecasting.
\nAfter performing a number of experiments, the data set of financial indicators was found using which FNN made the best forecast. These indicators are the following:
debt/assets = (short-term debt + long-term debt)/total assets;
loans to deposits ratio;
net interest margin (NIM) = net interest income/earning assets;
return on equity (ROE) = net income/stockholder equity;
return on assets (ROA) = net income/assets equity;
cost/income = operating expenses/operating income; and
equity/assets = total equity/total assets.
A series of experiments was carried out for determining the influence of the number of rules and period of data collection on forecasting results.
\nIn the first series of experiments, FNN TSK was used for forecasting.
\nExperiment Nos. 1–5:
Training sample = 115 banks of Europe, testing sample = 50 banks, and number of rules = 5.
Input data period = 2004 (experiment 1), 2005 (experiment 2), 2006 (experiment 3), 2007 (experiment 4), and 2007 (experiment 5).
The total results of application FNN TSK for different rules number and data collection period are presented in Table 20.
\nExperiment/number of rules | \nTotal errors number | \n% of errors | \nNumber of first type errors | \nNumber of second type errors | \n
---|---|---|---|---|
2004—5 | \n8 | \n16 | \n0 | \n8 | \n
2005—5 | \n7 | \n14 | \n0 | \n7 | \n
2006—5 | \n5 | \n10 | \n0 | \n5 | \n
2007—5 | \n1 | \n2 | \n0 | \n1 | \n
2004—10 | \n8 | \n16 | \n0 | \n8 | \n
2005—10 | \n8 | \n16 | \n1 | \n7 | \n
2006—10 | \n11 | \n22 | \n7 | \n4 | \n
2007—10 | \n4 | \n8 | \n0 | \n4 | \n
Forecasting results for FNN TSK versus number of rules and data period.
Furthermore, the similar experiments were performed with FNN ANFIS, while the period of data collection varied since 2004–2007. The corresponding results for FNN ANFIS are presented in Table 21 showing the influence of data collection period on forecasting accuracy.
\nExperiment/number of rules | \nTotal errors number | \n%% of errors | \nNumber of first type errors | \nNumber of second type errors | \n
---|---|---|---|---|
2004—5 | \n8 | \n16% | \n0 | \n8 | \n
2005—5 | \n8 | \n16% | \n1 | \n7 | \n
2006—5 | \n8 | \n16% | \n4 | \n4 | \n
2007—5 | \n4 | \n8% | \n0 | \n4 | \n
Forecasting results for FNN ANFIS versus number of rules and data period.
After analysis of these results, the following conclusions were made:
FNN TSK has better forecasting accuracy than FNN ANFIS;
the best input variables (indicators) for European banks bankruptcy risk forecasting are the following:
debt/assets = (short-term debt + long-term debt)/total assets;
loans to deposits;
net interest margin (NIM) = net interest income/earning assets;
return on equity (ROE) = net income/stockholder equity;
return on assets (ROA) = net income/assets equity;
cost/income = operating expenses/operating income; and
equity/assets = total equity/total assets.
Input data collection period (forecasting interval) makes influence on forecasting results.
\nIn next experiments, Fuzzy Group Method of Data Handling (FGMDH) was applied for European banks financial state forecasting. Fuzzy GMDH enables to construct forecasting models using experimental data automatically without expert [3]. The additional advantage of FGMDH is possibility to work with the fuzzy information.
\nAs the input data in these experiments, the same indicators as in experiments with FNN TSK were used. In Table 22, forecasting results are presented in dependence on input data period collection for FGMDH
\nInput data period | \nTotal number of errors | \n% of errors | \nNumber of first type errors | \nNumber of second type errors | \n
---|---|---|---|---|
2004 | \n7 | \n14 | \n0 | \n7 | \n
2005 | \n6 | \n12 | \n1 | \n5 | \n
2006 | \n4 | \n8 | \n1 | \n3 | \n
2007 | \n2 | \n4 | \n0 | \n2 | \n
Comparative analysis of forecasting results for FGMDH.
If to compare the results of FGMDH with the results of FNN TSK, one can see that neural network has better accuracy at the short forecasting interval (1 year), while fuzzy GMDH has better accuracy at the greater intervals (2 or more years). This conclusion coincides with similar conclusion for Ukrainian banks.
\nIn Table 23, the comparative results of application of different methods for bankruptcy risk forecasting are presented
\nMethod (period) | \nTotal number of errors | \n% of errors | \nNumber of first type errors | \nNumber of second type errors | \n
---|---|---|---|---|
ANFIS (1 year) | \n4 | \n8 | \n0 | \n4 | \n
TSK (1 year) | \n1 | \n2 | \n0 | \n1 | \n
FGMDH (1 year) | \n2 | \n4 | \n0 | \n2 | \n
ANFIS (2 years) | \n8 | \n16 | \n4 | \n4 | \n
TSK (2 years) | \n5 | \n10 | \n0 | \n5 | \n
FGMDH (2 years) | \n4 | \n8 | \n1 | \n3 | \n
Forecasting results of different fuzzy methods.
For estimation of fuzzy methods’ efficiency at the problem of bankruptcy risk forecasting the comparison with crisp method, the regression analysis of linear models was performed. As input data, the same indicators were used, which were found optimal for FNN. Additionally, the index net financial result was also included in the input set. This index makes great impact on forecasting results. Thus, input data in these experiments were eight financial indicators of 256 European banks according to their reports:
debt/assets—X1;
loans/deposits—X2;
net interest margin—X3;
ROE (return on equity)—X4;
ROA (return on assets)—X5;
cost/income—X6;
equity/assets—X7; and
net financial result—X8.
The input data were normalized before the application. The experiments were carried out with full regression ARMA model, which used eight variables and shortened models with six and four variables.
\nEach obtained model was checked on testing sample consisting of 50 banks. The comparative forecasting results for all ARMA models are presented in Table 24.
\nInput data | \nTesting sample | \nFirst type of errors | \nSecond type of errors | \nTotal number of errors | \n% of errors | \n
---|---|---|---|---|---|
All variables (eight) | \n50 | \n5 | \n4 | \n9 | \n18 | \n
Six variables | \n50 | \n5 | \n4 | \n9 | \n18 | \n
Four variables | \n50 | \n5 | \n4 | \n9 | \n18 | \n
Comparative analysis of ARMA models.
As one may see in Table 24, the application of all types of linear regression models gives the same error of 18%, which is much worse than application of fuzzy neural networks.
\nFurthermore, the experiments were performed using logit models for bankruptcy forecasting [9, 10]. The training sample consisted of 165 banks and the testing sample of 50 banks.
\nThe first one was constructed, linear logit model, using all the input variables. It has the following form (estimating and forecasting equations):
\nThe next constructed model was a linear probabilistic logit model with six independent variables. The final table including the forecasting results of all the logit models is presented below (Table 25)
\nInput data | \nTesting sample | \nFirst type of errors | \nSecond type of errors | \nTotal number of errors | \n% of errors | \n
---|---|---|---|---|---|
All variables (eight) | \n50 | \n6 | \n2 | \n8 | \n16 | \n
Six variables | \n50 | \n6 | \n2 | \n8 | \n16 | \n
Comparative analysis of logit models.
The next experiments were carried out with probit models [9, 10]. The first constructed model was the linear probit model based on 206 banks using all the input variables. It has the following form:
\nAs the experiments had shown that the inputs net interest margin (\n
Furthermore, in this model insignificant variables debt/assets (\n
Each of the constructed probit models was checked on the test sample of 50 banks. The results of application of all probit models are presented in Table 26.
\nInput data | \nTesting sample | \nFirst type of errors | \nSecond type of errors | \nTotal number of errors | \n% of errors | \n
---|---|---|---|---|---|
All variables (eight) | \n50 | \n5 | \n2 | \n7 | \n14 | \n
Six variables | \n50 | \n5 | \n2 | \n7 | \n14 | \n
Four variables | \n50 | \n6 | \n3 | \n9 | \n18 | \n
Forecasting results of probit models.
As one may see from Table 26, the application of all the probit models gives relative error 14–18%, which is much worse than results obtained by fuzzy neural networks. It is worth to mention the decrease of model forecasting quality after exclusion of insignificant variables.
\nIn the final series of experiments, investigations and detailed analysis of various methods for forecasting bankruptcy risk were performed. The following methods were investigated: FNN ANFIS, FNN TSK, FGMDH, regression models, logit models, and probit models.
\nPeriod of input data was 2007 (1 year before possible bankruptcy).
\nComparative analysis of all the forecasting methods is presented in Table 27.
\nMethod | \nTotal number of errors | \n% of errors | \nFirst type of errors | \nSecond type of errors | \n
---|---|---|---|---|
ANFIS | \n4 | \n8 | \n0 | \n4 | \n
TSK | \n1 | \n2 | \n0 | \n1 | \n
FGMDH | \n2 | \n4 | \n0 | \n2 | \n
ARMA | \n9 | \n18 | \n4 | \n5 | \n
Logit | \n8 | \n16 | \n2 | \n6 | \n
Probit | \n7 | \n14 | \n2 | \n5 | \n
Comparative analysis of methods for banks bankruptcy forecasting.
As one may see from this table, fuzzy methods and models show much better results than crisp methods: ARMA, logit models, and probit models. When forecasting by one year prior to current date, fuzzy neural network TSK shows better results than FGMDH. But when forecasting for longer intervals (several years), FGMDH is the best method.
\nIn a whole, the conclusions of experiments with European banks completely confirmed the conclusions of experiments with Ukrainian banks.
\nThe problem of banks bankruptcy risk forecasting under uncertainty was considered.
\nFor its solution, the application of novel methods of computational intelligence, fuzzy neural networks ANFIS and TSK and fuzzy GMDH, was suggested.
The experimental investigation of FNN TSK, ANFIS, and GMDH application in the problem of bankruptcy risk forecasting was carried out for Ukrainian and European banks.
The comparison of forecasting efficiency of FNN TSK and ANFIS with Fuzzy GMDH and conventional statistical methods ARMA, logit, and probit models was performed.
The experimental results show that FNN and FGMDH have much better accuracy than statistical methods. When forecasting by one year prior to current date, fuzzy neural network TSK shows better results than FGMDH. But when forecasting for longer intervals (several years), FGMDH is the best method.
While in experimental investigations, the best sets of financial indicators for bankruptcy forecasting were found for Ukrainian and European banks as well.
Small scale combustion appliances are mainly used for the purpose of residential heating. Several studies show that combustion of biomass fuels in small scale heating appliances is a common source of both particulate matter (PM) and gaseous emissions such as fine particles, polycyclic aromatic hydrocarbons (PAH), volatile organic compounds (VOC) and carbon monoxide, carbon dioxide, nitrogen oxide, sulfur oxide, etc. [1, 2, 3, 4, 5, 6, 7, 8]. PM is a dynamic mixture of particles in the flue gas released directly from the combustion devices. The aerodynamic diameter is generally used to indicate the particle size since the particles have different shapes and densities. It is defined as the diameter of a spherical particle with a mass density of 1000 kg/m3 that has the same inertial properties in the flue gases [9, 10, 11]. Several particles size fractions of PM are defined in the literature: PM0.1 (nano particles: <0.1 μm), PM1 (ultrafine particles: <1 μm), PM2.5 (fine particles: <2.5 μm), PM10 (coarse particles: <10 μm) [9, 10, 12].
In comparison to liquid and gaseous fuels, the emissions of particulate matter from biomass combustion are high [9, 13, 14, 15, 16, 17]. Majority of the particles is less than 1 μm (micrometer) in size and emitted straight away to the ambient air from the combustion appliances [18, 19]. Numerous studies have demonstrated that increased particle emissions in the ambient air correlate with severe health effects in the exposed population, including respiratory and cardiovascular illnesses as well as increased mortality [15, 20, 21]. Further, it has been mentioned that in the case of combustion related fine particle fraction is more dangerous to human health and environmental effects [2, 15, 20, 21, 22].
Using wood pellets as biomass fuel is gradually increasing due to their high energy density, easy transportability and the lower amount of gas emissions from its production and transportation comparing to oil, coal and natural gas [23]. Nowadays, combustion of wood pellets in small scale heating appliances is efficient and produces significantly lower emissions than the old wood log combustion appliances [4].
Most of the heating appliances in the market claim an optimized combustion with low emissions of gaseous pollutants at nominal operational load. However, operation at full load is only required for a short peak winter period [4]. For the rest of the year, the combustion appliances may work at lower operational loads as far as continuous operation is considered. The emissions of these pollutants are significantly different if the heating appliance is operating at lower loads i.e. part load. Carbon monoxide (CO) emissions from residential pellet heating devices mainly report during stationary operation, however, a considerable part of un-burnt fuels is emitted during the startup and burnout phases [24, 25].
This chapter presents the experimental results regarding particle and gaseous emissions from a modern bottom feed pellet stove operated with nominal load (5 kW) and part load (2.5 kW) heat output. The particle emission measurements include mass concentrations of PM1 and PM2.5, number concentrations and their particle size distributions measured continuously using a partial flow dilution tunnel together with an Electrical Low Pressure Impactor Plus (ELPI+) with a flow rate 10 lpm and cut-off size of the 14 stages from 6 nm to 10 μm.
This section briefly discusses the previous work on particle emissions, experimental setup, fuel characteristics and combustion appliance related to the emissions measurements.
There is lack of information regarding the characterization of particulate emissions from small scale biomass combustion. Several studies on particle emission from biomass stoves were carried out in EU countries. For example, Boman et al. [26] investigated six types of different pellet fuels in three different commercial pellet burners (10–15 kW) and observed that fine particles (<1 μm) contain a significant part of the total PM emissions.
Sippula et al. [27] investigated the effect of wood pellet combustion on the particle emissions from a top feed pellet stove with a heat output of 8 kW using an ELPI. Their results show that particle number emissions varied from 1.3 × 107 to 4.4 × 107 particles/cm3 and the PM1 varied from 69 to 343 mg/Nm3. Gaegauf et al. [28] investigated particle emissions by using an SMPS on a pellet boiler with a capacity of 17 kW. They observed that the major part of the particle emissions were in the range between 30 and 300 nm.
Bari et al. [29] studied particle mass and number emissions from a pellet stove with a nominal output of 5 kW. The measurements were conducted from the stack using a Berner Low Pressure impactor (BLPI) and a Scanning Mobility Particle Sizer (SMPS) for mass concentrations and number size distributions respectively. The results show that the PM10 concentrations were between 31 and 201 mg/Nm3, while number concentrations varied between 1.5 × 107 and 5.4 × 107 particles/cm3. They observed that the particle mass size distributions were unimodal with maximum concentrations in the fine fraction.
Bäfver et al. [30] experimentally studied particle and CO emissions from modern and old type residential stoves of various heat capacity fired with wood logs and wood pellets. Measurements were performed using a Dekati Low Pressure Impactor (DLPI) for mass size distribution while an ELPI was used for number size distributions. Modern pellets stoves showed lower mass concentration of particles as well as lower CO concentrations than the old type wood stoves. They found that in all cases, the particle mass emissions were dominated by fine particles and there was only small fraction of coarse particles.
Qie et al. [31] studied particle emissions in a small scale pellet boiler (50 kW) using a Dust Trak-II Handheld Aerosol Monitor from 100 nm to 10 μm. Three types of biomass pellets, i.e. wood pellets, Miscanthus pellets and straw pellets were combusted. PM10 concentrations of wood pellets, Miscanthus pellets and straw pellets were 72.7, 100 and 150 mg/Nm3, respectively. PM concentration results show that wood pellets are better than Miscanthus and straw pellets.
Johansson et al. [32] investigated particle emissions from a domestic pellet stove with a capacity of 6 kW. The stove was fired with wood pellets. Particle characterizations were done with an Electrical Low Pressure Impactor (ELPI). PM10 mass concentration was 47 mg/Nm3, number concentrations varied between 1.8 × 107 and 8.7 × 107 particles/cm3.
The above review briefly illustrates that a number of studies on particulate matter concentrations related to the small scale heating appliances at nominal load operations [19, 27, 33, 34]. Particle emissions from residential heating devices are documented mainly for stationary operation, however a considerable part of un-burnt fuels are emitted during the startup and burnout phases. PM emission characteristics at each phase of pellet stove operations are therefore important to be able to reduce the annual emissions from residential pellet combustion.
The measurements were conducted according to the European standard EN 14785 for residential space heating appliances fired by wood pellets [35]. Two experiments (A and B) in part load and four experiments (C, D, E and F) in nominal load heat output were conducted for the emissions measurements from a bottom feed modern pellet stove. The stove was operated in different fan speeds, which regulate air flow into the combustion chamber. Experiments A and B were operated with low speed fan at 900 rpm, C and D with medium speed fan at 1250 rpm, E and F with high speed fan at 1400 rpm. Fan speed settings of each experiment are presented in Table 1. The wood pellets are transported through two screws from the pellet storage hopper to the burner cup. The rotation of screw-1 connected to the pellet storage hopper was 1.6/6 sec for the part load measurements, while 3.2/6 sec for the nominal load experiments. Screw-2 connected to the burner cup was operated at 2 rpm for all the experiments. The heat output of the stove was modified by controlling the rotation of screw-1, which controls the fuel supply.
The elemental composition, moisture content and lower heating value (LHV) of the commercial pellets used in the combustion experiments are presented in Table 2. The pellets are made from soft wood, certified by DINPlus standard and available in the European market.
Parameter | Commercial pellets | DINplus |
---|---|---|
Length (mm) | <45 | <45 |
Diameter (mm) | 6.06 ± 0.1 | 6 ± 0.5 |
Durability (%) | 98.9 | >97.7 |
Fine content (%) | 0.13 | <1 |
Volumetric mass (kg/m3) | 675 | >650 |
LHV (MJ/kg) | 18.7 | >16.9 |
Moisture (%) | 8.6 | 10 |
Ash (wt %) | 0.3 | 0.7 |
C (wt %) | 49.1 | — |
H (wt %) | 5.8 | — |
O (wt %) | 44.8 | — |
The combustion appliance used in the experiments was a bottom feed pellet stove with a nominal heat output of 5 kW. The pellet stove was setup on a balance to monitor the fuel consumption. The pellet stove is equipped with an internal pellet storage, where the pellets are supplied through two screws into the burner cup. The combustion takes place in the burner cup. A step motor is used to supply the pellet into the combustion chamber. The combustion air consisting of primary and secondary air is supplied through the holes under the grid of the burner cup. The air supply is fan assisted and depends upon the selected thermal output. A short cleaning period is set to occur every 30 min in the stove. During cleaning, the fuel supply decreases and the air supply increases for 1 min, removing the ash gathered on the grid. The front side of the stove is covered with a high temperature transparent glass window. The top of the combustion chamber is equipped with the baffle plate made of vermiculite materials and the sides of refractory ceramic bricks made of calcium silicate. The flue gases are drawn out by an exhaust fan.
A partial flow from the stack at about 2 m height from the pellet stove was withdrawn through an externally insulated steel probe of 12 mm diameter. The opening of the probe was positioned towards the flow of the stack. The CO emissions were analyzed continuously from the flue gas by a Siemens Ultramat 6 gas analyzer, CO2 and O2 concentrations were measured continuously using a Horiba PG-250 gas analyzer. Both gas analyzers cannot withstand the hot and humid flue gases for direct analysis. Before the analyzers, the flue gas samples passed through the chiller to remove moisture and to cool down the gas. The gas analyzers were calibrated with an appropriate gas mixture, before and after each combustion experiment. The measurement principles of the gas analyzers were galvanic analyzer for O2 and non-dispersive infra-red for CO, CO2. The analyzers have the measurement error of ±2% full scale in linearity and ± 0.5% full scale in repeatability. Temperature of the indoor air and flue gas in the stack were measured by the K-type thermocouples.
Particle emissions were measured continuously from a partial flow dilution tunnel using an ELPI+ with a flow rate 10 lpm and cut-off size of the 14 stages from 6 nm to 10 μm. Sample particles entering the ELPI+ are first charged in the charger. The charged particles collected in each impactor stage produce an electrical current which is recorded by the respective electrometer channel. This current is proportional to particle numbers via mathematical algorithms [36]. Aluminum foils, greased with a mixture of acetone and Apiezon-L were placed on each of the impactor stages to prevent particle bouncing effects. The flue gases were diluted through a two steps partial flow dilution tunnel with pre-filtered dilution air before reaching the ELPI+. The dilution tunnel consists of a porous tube diluter (PRD), an ejector diluter (ED) and an air heater. The first stage dilution air injected (17.5 lpm) into the PRD was heated to match the raw sample temperature to reduce the risk of condensation. The second stage dilution air injected (49 lpm) into the ED, which was operated at ambient temperature to further dilute the sample and to reduce the sample temperature to the ambient condition. Dilution air is taken from outside the building to simulate the field conditions.
The CO2 and O2 concentration from the undiluted flue gas were analyzed continuously by a Horiba PG250 gas analyzer. CO2 concentration was also measured continuously from the diluted sample by a Vaisala Carbocap analyzer to calculate the dilution ratio (DR). The details of the DR measurement were presented other works [4, 5, 37, 38].
A total of six combustion experiments on gaseous and particle emissions from a bottom feed pellet stove were conducted. As the objectives of this chapter were to evaluate the emissions from different combustion phases of each experiment, the emission results from each experiment are presented as the startup, the combustion and the burnout phases.
The CO emissions obtained from the startup, combustion, burnout phase of all the experiments are presented in Figures 1–3 respectively. The error bars present the uncertainty of the measurements. The CO emission values presented here are normalized with 13% dry oxygen content. It is clearly observed from all the experiments that CO emissions in the burnout phase were significantly higher than that in the startup phase followed by the combustion phase. The air excess (λ) in the burnout phase for all the experiments was quite higher than that in the other two phases. High excess air in the burnout phase cools the combustion chamber, resulting in high CO emissions.
CO emissions obtained from the startup phase of all the experiments [7].
Comparison of CO emissions obtained from the combustion phase of all experiments with the standard [7].
CO emissions obtained from the burnout phase of all experiments [7].
It can be seen from Figure 1 that the CO emissions obtained from the startup phase of the part load heat output varied from 1710 to 2370 mg/Nm3 for experiments A to B, while in the nominal load heat output varied from 908 to 2294 mg/Nm3 for the experiments C to F. The duration of startup phase is about 20 min for all the experiments. The stove operated in the medium speed fan gives lower CO emission in the startup phase. However, CO emissions in the startup phase for the experiments E and F were higher than the measurements C to D. At the startup phase, the combustion temperature was not high enough to provide sufficient burnout condition. This might be a reason for increasing CO emissions during the startup phase.
Figure 2 shows the comparison of CO emissions obtained from the main combustion phase of all the experiments with the required limit value of the NBN EN 14785 standard and the literature [39]. CO emission in Y axis is presented in logarithm scale. The CO emissions from the medium and high speed fan stove operated with nominal load output satisfied the required limit value of the NBN EN 13229 standard and lower than other work [39]. CO emissions obtained from the low speed fan operated with part load heat output did not meet the required limit value of the standard.
It can also be seen from Figure 2 that the CO emissions obtained from the main combustion phase of the part load heat output varied from 1215 to 1450 mg/Nm3 for experiments A and B, while in the nominal load heat output varied from 50 to 145 mg/Nm3 for the experiments C to F. The duration of the main combustion phase varied from 3 h 50 min to 5 h 45 min for all the measurements. The lower CO emissions obtained from the stove operated with high speed fan than the medium speed fan followed by the low speed fan. Higher CO emission in the part load experiments was probably due to the higher air excess factor (about λ = 4.35) obtained in low speed fan, which gives lower combustion temperature, leading to high CO emissions. On the other hand, a correctly matched air excess factor (about λ = 2.5) for the medium and high speed fan operated experiments created favorable combustion conditions, leading to less CO emissions. Besides, the average flue gas temperature was much lower in the low speed fan (64°C) operated experiments than the medium speed (85°C) and high speed fan (101°C).
It can be seen from Figure 3 that experiments E and F had the lower CO emissions in the burnout phase because of the different configuration of the fan speed from other measurements A, B, C and D. Also, the fan speeds for the experiments E and F were higher than the other experiments. This means that sufficient amounts of combustion air were supplied to burn the combustible gases; as a result, CO emissions were lower. Experiments conducted in the high speed fan gives lower CO emission in the burnout phase.
The total CO emissions showing in Figure 4 are relatively higher in part load combustion experiments compared to nominal load output. This was due to the lower combustion temperatures caused by high air excess at the part load combustion experiments. The total CO emissions obtained in the part load experiments can be compared with values found in other work. For example, Schmidl et al. [40] investigated gaseous emissions from a 3 kW pellet stove in part load power output. The CO emissions in their study were 751 mg/Nm3 which is quite lower than that in our study. The total CO emissions obtained from the nominal load output experiments are higher than other studies. For example, the CO emissions results of Bäfver et al. [30] investigated from a pellet stove with 5 kW capacity range between 140 and 405 mg/Nm3.
Total CO emissions obtained from all the experiments [7].
It is clearly observed that CO emissions in the burnout phase from all the experiments were significantly higher than that in the startup phase followed by the combustion phase. For example, CO emissions in the burnout phase for experiments C to D were about 12 fold higher than in the startup phase and 75 fold higher than in the combustion phase. The air excess (λ) in the burnout phase for all the experiments was quite higher than that in the other two phases. High excess air in the burnout phase cools the combustion chamber, resulting in high CO emissions. It can be mentioned from the experimental results that the impact of higher CO emissions in the startup and burnout phase has influence on the total CO emissions.
Several studies [34, 41, 42] mention that higher combustion temperature, better turbulence mixing fuel with necessary oxygen and sufficient residence time can play a major role in combustion optimization and consequently emissions reduction. The CO emissions from a combustion device might represent the incomplete combustion caused by low combustion temperature, insufficient oxygen, short residence time, poor fuel and air mixing or a combination of these factors [34, 43].
CO emissions from small scale biomass combustion appliances can be reduced using flue gas cleaning technologies such as catalytic combustors, which consist of a metal wire mesh covered with catalytic material, platinum and palladium. The catalytic combustors are attached to a steel frame which can be inserted compactly inside the stack through an opening. Smoke gases pass through the catalytic element and ignite at a much lower temperature around 250°C. The result is that harmful substances are more completely burned. The fuel produces more heat through an extended clean burn. Hukkanen et al. [44] investigated reduction of gaseous emissions using a catalytic combustor from a 15 kW stove. Their results show that reductions of CO reached about 25% during the whole combustion cycle. Such gas cleaning systems are however quite expensive for small scale applications.
Figures 5 and 6 present the comparison of particle mass concentrations of PM1 and PM2.5 obtained from the startup, combustion, burnout phases and the total cycle of all the combustion experiments. Figure 5 shows PM1 concentrations obtained from the startup phase of the part load heat output. Experiments A to B varied from 26.1 to 38.4 mg/Nm3 for the startup phase, 20.4 to 29.8 mg/Nm3 for the combustion phase, 9.3 to 10.2 mg/Nm3 for the burnout phase and 20.5 to 27.6 mg/Nm3 for the total cycle, while in the nominal load heat output experiments C to F varied from 22 to 106 mg/Nm3 for the startup phase, 43.3 to 276 mg/Nm3 for the combustion phase, 4.7 to 12 mg/Nm3 for the burnout phase and 44 to 236 mg/Nm3 for the total cycle.
Comparison of PM1 concentrations obtained from all the combustion experiments [17].
Comparison of PM2.5 concentrations obtained from all the combustion experiments [17].
The PM1 results obtained from the combustion phase in nominal load output of experiments C and D are significantly higher than those from the other experiments. In the part load heat output measurements, the startup phase of experiment A gave the highest PM1 emissions. The variation of particle mass concentrations among all the experiments is due to the configuration of the burner, which operated with the different fan speeds.
The particle mass emissions reported by Sippula et al. [27], Johansson et al. [18] were also measured in a partial flow dilution tunnel. It should be mentioned that some conditions in the sampling line such as the dilution ratio, temperature and the measurement equipments were different. Therefore, it is difficult to formulate a direct comparison of the particle emissions results. Our particle mass concentration results for the PM1 fraction obtained from the combustion phase in nominal load heat output can be compared with results from another study. For example, Sippula et al. [27] investigated particle mass emissions from a top feed pellet stove with a heat capacity of 8 kW using filter samples. Average mass concentrations of PM1 in their study varied between 69 and 343 mg/Nm3 which are slightly higher values than in our study.
Figure 6 shows the comparison of PM2.5 concentrations obtained from different experiments at nominal load and part load heat output. In part load experiments, PM2.5 concentrations varied from 45.3 to 57.8 mg/Nm3 for the startup phase, 34.4 to 48 mg/Nm3 for the combustion phase, 17 to 18 mg/Nm3 for the burnout phase and 34.2 to 45 mg/Nm3 for the total cycle, while in the nominal load experiments, varied from 61.5 to 138 mg/Nm3 for the startup phase, 66 to 436 mg/Nm3 for the combustion phase, 10.3 to 26.3 mg/Nm3 for the burnout phase and 65.7 to 373 mg/Nm3 for the total cycle.
It is observed that the particle mass fractions of PM1 and PM2.5 concentrations from the experiments operated with medium fan speed are about 4-folds higher than the high speed fan experiments. This might be due to the lower air excess factor λ = 2.8 for the medium speed fan experiments, while λ = 2.4 for the high speed fan experiments, which gives higher combustion temperature and creates favorable combustion condition.
In nominal load experiments C, D and E, particle mass fractions of PM1 and PM2.5 obtained from the combustion phase are significantly higher than in the other two phases of startup and burnout. The PM1 and PM2.5 concentration levels can also vary from one experiment to another, which are typical for the biomass combustion. The PM1 concentrations of all the nominal load experiments accounted for 61, 68 and 50% of the PM2.5 concentrations for the startup, combustion and burnout phase respectively, while 62, 61 and 55% for the part load experiments, which are lower than the values found in literature [26]. This analysis from both nominal and part load het output experiments clearly shows that more than 50% of particle mass concentrations is the fine fractions of PM1.
It is reported in the literature that the fine particle mass fractions (PM1 and PM2.5) are generally formed from easily volatile inorganic species (K, S, Na and Cl) and heavy metal elements (Zn and Pb) that have vaporized during combustion, which later saturate and form fine particles by nucleation. The nucleated particles grow further by coagulation, agglomeration, condensation and surface reactions. In the gas phase, these species undergo reactions resulting in the formation of alkaline metal sulphates, chlorides and carbonates as well as heavy metal oxides. Organic species represent the fraction of fine particle emissions. These particles are mainly due to incomplete combustion and to the condensation of the unburned hydrocarbon during the cooling phase of the flue gas [9, 10, 12, 27, 45].
Figures 7–9 present the particle mass size distribution graphs obtained from the startup, combustion and burnout phases of all the experiments respectively. The abscissa represents the particle aerodynamic diameter against the ordinate which shows the ratio of particle mass concentration dM to the logarithm of the channel width dlog(Dp), where Dp is the aerodynamic diameter.
Particle mass size distributions obtained from the startup phase of all the experiments [17].
Particle mass size distributions obtained from the combustion phase of all the experiments [17].
Particle mass size distributions obtained from the burnout phase of all the experiments [17].
Figure 7 shows that maximum particle concentrations obtained for all the experiments in the fine mode are at the particle size of 320 nm. Particle size between 10 and 80 nm contains very small amounts of mass and are probably soot particles, therefore these particles are not seen in the mass size distribution graphs. Figure 8 shows that experiments A, B, E and F had quite similar mass size distributions, with maximum particle concentrations in the fine mode at the particle size of 320 nm, while experiments C and D had the peak particle emissions at the particle size of 750 nm.
In Figure 9, it can be seen that particle mass size distributions of all the experiments (except experiments C and D) from the burnout phase are quite similar with a maximum particle concentration at the particle size of 320 nm. The mass size distributions graphs showed that all the experiments had a fraction of particles appearing in the coarse mode.
Figure 10 shows the comparison of particle number concentrations obtained from the startup, combustion, burnout and total cycle of all the experiments. Particle number concentrations obtained from the part load experiments A and B varied from 9.5 × 106 to 1.2 × 107 particles/cm3 for the main combustion phase and 1.0 × 107 to 1.3 × 107 particles/cm3 for the total cycle, while in the nominal load heat output experiments C, D, E and F varied from 1.4 × 107 to 8.8 × 107 particles/cm3 for the combustion phase and 1.4 × 107 to 7.6 × 107 particles/cm3 for the total cycle. Particle number emissions from the startup and burnout phase have the less impact on the total particle number emissions.
Comparison of particle number concentrations [17].
The duration of the main combustion phase varied from 3 h 50 min to 5 h 45 min for all the measurements. In the nominal load output for the combustion experiments C and D of the pellet stove, it can be seen from Figure 10 that the combustion phase had the highest particle number concentrations, followed by the startup phase and the burnout phase, while for the combustion experiments E and F and part load experiments A and B had the highest particle number concentrations occurred in startup phase followed by the combustion phase and the burnout phase. This is because the configuration of the burner operated with the different fan speed used in the experiments.
Experiments operated with nominal load heat output, much lower particle number emissions obtained from the stove operated with high speed fan experiments E and F than the medium speed fan experiments C and D. This could be explained lower air excess factor λ = 2.8 for the medium speed fan experiments, while λ = 2.4 for the high speed fan experiments. Besides, the average flue gas temperature was 85°C for the medium speed experiments and 101°C for the high speed fan experiments. The number concentrations from the main combustion of the part load experiments were much lower than nominal load experiments. This may be due to the difference of fuel consumption, fan speed of the screw, which regulates air flow into the combustion chamber and heat output. The average fuel consumption for part load experiments is about one-half lower than the nominal load experiments, which might impact on particle emissions.
The particle number concentrations obtained in this study can be compared with other studies. For example, Sippula et al. [27] investigated the effect on particle number concentrations from a top feed pellet stove with a capacity of 8 kW in nominal load output using an ELPI. Their results show that particle number emissions varied from 1.3 × 107 to 4.4 × 107 particles/cm3, which is a little lower than the values obtained in our measurements in the combustion phase at nominal heat output. In another study, Bari et al. [29] studied particle number concentrations from a 5 kW pellet using a SMPS instrument. Their results show that particle number concentrations varied between 1.5 × 107 and 5.4 × 107 particles/cm3, which is also little lower than the values obtained in our study. Since the fine particles are believed to be more harmful, more attention should be given to fine particle regulation. The EU standards describe the particle emissions in terms of mass concentration [46, 47], however, current research demonstrates that particle number emissions and particle size distributions are very important when considering particle impacts on air quality, climate, environment and human health [21, 48]. The emissions of particle concentration are strongly dependent on combustion conditions, fuel properties, combustion appliances, excess air, heat output of the combustion technology, etc. Small scale biomass combustion is generally considered as an important source of fine particles due to the lack of cleaning systems.
Typical particle number size distributions obtained from the startup, combustion and burnout phases of all the combustion experiments are presented in Figures 11–13. Figure 11 shows that the peak in particle number concentrations was observed at the particle size from 25 to 70 nm for the startup phases of all the combustion experiments. A uni-modal peak can be seen in the experiments C and D, while bimodal size distributions were appeared in the other combustion experiments.
Particle number size from distributions obtained from the startup phase of all the experiments [17].
Similar particle number size distributions were observed in other studies. For example, Bari et al. [29] investigated particle number size distributions from a pellet stove of 5 kW nominal output using a SMPS. Their results show that the maximum number particle concentrations were found at the particle size within the diameter range from 55 to 90 nm. Boman et al. [49] investigated particle number size distributions from a pellet stove of capacity 5 kW using a SMPS and their results show that maximum particle at the particle size was about 70–80 nm.
Figure 12 presents the particle number size distributions graphs for the combustion phase and it can be seen that the emitted particles for all the experiments were very similar with the startup phase and peak particle number concentrations were at the particle size around 70–100 nm. In contrast to the startup phase, the maximum particle concentrations shifted to larger particle sizes. The measured particle number concentrations for combustion experiments C and D were significantly higher operated with medium fan speed than that high speed fan experiments followed by the low speed fan experiments.
Particle number size from distributions obtained from the combustion phase of all the experiments [17].
Figure 13 presents the particle number size distributions for the burnout phase, where the maximum particle number concentrations were observed between 20 nm and 80 nm. The combustion experiments C and D had uni-modal size distributions, while the remaining experiments had bi-modal size distributions. The fine particles size less than 1 μm are formed from the easily volatile inorganic elements, released from the biomass fuels to the gas phase during combustion. Potassium, sulfur and chlorine are the most relevant element during the combustion of biomass fuels. These small size particles are considered very harmful for human health as they penetrate lower the alveolar region of the lung. Particles with diameter below 100 nm are the most important when considering the number distributions, but it contributes on only a very small fraction of the total mass. Fine particles originated from small scale biomass combustion mainly consist of ash, elemental carbon and organic material [9, 14]. Particle emissions are dominated by ash particles when the combustion quality is good, for example as in pellet combustion.
Particle number size distributions obtained from burnout phase of all the experiments [17].
The performance analysis in terms of combustion efficiency of the pellet stove was determined using an indirect method according to the standard EN 14785 that takes the thermal, chemical and radiation heat losses into consideration [35]. Efficiency was determined according to the difference between energy input and the sum of the losses. The thermal heat loss was evaluated on the basis of the difference between the temperature of the flue gas and the room temperature and the specific heat of the flue gas. The chemical heat loss is calculated from the CO and CO2 concentrations of the flue gas. The radiation heat loss is taken as 0.2% according to the standard EN 14785. The formulas used for the calculation of the combustion efficiency and the different losses were discussed in the works [4, 7].
The combustion efficiency of the pellet stove as a function of different operational loads is compared with the required limit value of the standard NBN EN 14785 and presented in Figure 14. It can be seen from the figure that all the measurements both from nominal heat and part load output meet the standard. All the experiments have almost similar combustion efficiencies at both operational loads. The average combustion efficiency obtained from all the experiments for the low speed fan, medium speed fan and high speed fan was 92.8 ± 1.2, 92.4 ± 1.1 and 92.7 ± 1.2% respectively. The average thermal heat and chemical heat losses are estimated at 6.05 and 0.93% respectively for the low speed fan, 6.95 and 0.22% respectively for the medium speed fan and 6.95 and 0.14% respectively for the high speed fan, which influences the variations of the combustion efficiency as seen from Figure 14. Experiment B had the highest combustion efficiency from the part load operated with low speed fan, while experiments C and E had the higher efficiency from the nominal load output.
Combustion efficiency compared with the standard [7].
The combustion efficiency evaluated from the experiments in nominal load heat output can be compared with other works. For example, Sippula et al. [27] mentioned about 85% combustion efficiency from a 8 kW modern pellet stove in standard laboratory condition which is lower than this study.
A total of six combustion experiments on gaseous and particle emissions from a modern bottom feed pellet stove were conducted. Following conclusions can be drawn from this chapter.
CO emissions in the burnout phase from all the experiments were significantly higher than that in the startup phase followed by the combustion phase. CO emissions in the burnout phase for experiments C to D were about 12 fold higher than in the startup phase and 75 fold higher than in the combustion phase. The air excess (λ) in the burnout phase for all the experiments was quite higher than that in the other two phases. The experimental results show that the impact of higher CO emissions in the startup and burnout phase has influence to increase the total CO emissions.
The CO emissions obtained in the main combustion phase from the experiments conducted with high speed fan were lower than the medium speed fan followed by the low speed fan. Higher CO emission in the low speed fan was probably due to the higher air excess factor (about λ = 4.35), which gives lower combustion temperature, leading to high CO emissions.
For the nominal load experiments, the particle mass fractions of PM1 and PM2.5 obtained from the combustion phase are significantly higher than those in the other two phases (startup and burnout phase). But, in the part load experiments, PM1 emissions in the startup phase were relative higher than in the other phases.
Particle mass size distributions analysis showed that all the experiments have maximum particle concentrations in the fine mode mainly at the particle size about 320 nm for the startup and combustion phase and at 300 nm for the burnout phase.
The number concentrations from the main combustion of the part load experiments were much lower than nominal load experiments. This may be due to the difference of fuel consumption, fan speed of the screw, which regulate air flow into the combustion chamber and heat output.
Analysis from the particle number size distributions showed that maximum particle emissions were found for all the experiments between 25 and 70 nm for startup phase, 70 and 100 nm for the combustion phase and 20 nm and 80 nm for the burnout phase.
The author(s) gratefully acknowledge the support of the Erasmus Mundus External Cooperation Window of the European Commission and the European Regional Development Fund. The author(s) also would like to express sincere thanks to the entire Department of Mechanical Engineering, VUB, especially Prof. Dr. Svend Bram and the combustion laboratory of a stove manufacturing plant, Belgium for their cooperation in conducting the experiments.
The author declares no conflict of interest.
Berner low pressure impactor Dekati low pressure impactor ejector diluter European norms European union electrical low pressure impactor electrical low pressure impactor plus particle diameter dilution ratio hour lower heating value liter per minute polycyclic aromatic hydrocarbons particulate matter porous tube diluter rotation per minute scanning mobility particle sizer second volatile organic compounds micrometer nanometer milligram minute centimeter air excess degree celsius
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