Forecasting failure rate of water pipes

Abstract

This paper presents the results of failure rate prediction by means of support vector machines (SVM) – a non-parametric regression method. A hyperplane is used to divide the whole area in such a way that objects of different affiliation are separated from one another. The number of support vectors determines the complexity of the relations between dependent and independent variables. The calculations were performed using Statistical 12.0. Operational data for one selected zone of the water supply system for the period 2008–2014 were used for forecasting. The whole data set (in which data on distribution pipes were distinguished from those on house connections) for the years 2008–2014 was randomly divided into two subsets: a training subset – 75% (5 years) and a testing subset – 25% (2 years). Dependent variables (λr for the distribution pipes and λp for the house connections) were forecast using independent variables (the total length – Lr and Lp and number of failures – Nr and Np of the distribution pipes and the house connections, respectively). Four kinds of kernel functions (linear, polynomial, sigmoidal and radial basis functions) were applied. The SVM model based on the linear kernel function was found to be optimal for predicting the failure rate of each kind of water conduit. This model's maximum relative error of predicting failure rates λr and λp during the testing stage amounted to about 4% and 14%, respectively. The average experimental failure rates in the whole analysed period amounted to 0.18, 0.44, 0.17 and 0.24 fail./(km·year) for the distribution pipes, the house connections and the distribution pipes made of respectively PVC and cast iron.

Long-Term Trends in 20-Day Cumulative Precipitation for Residential Rainwater Harvesting in Poland

“…The study analysed the presence of trends in the rainfall time-series for 19 cities in Poland for years 1970-2019, from the perspective of design and operation of RWH systems. Therefore, there were analysed the 20-day cumulative rainfall periods along the year higher than the thresholds 10, 20, 30 and 40 mm, as well as the class intervals [0-10) mm, [10][11][12][13][14][15][16][17][18][19][20] mm, [20][21][22][23][24][25][26][27][28][29][30] mm and [30][31][32][33][34][35][36][37][38][39][40] mm. The results of the M-K test detected statistically significant (CLI ≥ 95%) or close to statistical significance (90% ≤ CLI < 95%) trends in 14 of the 152 datasets under analysis (9.2% of the total), and tendencies to change (75% ≤ CLI < 90%) in approximately 18% of the datasets, with less than half of them corresponding to downward trends.…”

“…1% 14% 26% 7% 5% 21% 34% 6% 6% 20% 31% 5% 7% 15% 30% 5% Gdańsk 2% 21% 48% 9% 12% 25% 42% 6% 8% 19% 30% 5% 2% 12% 25% 5% Gorzów Wlkp. 5% 16% 32% 7% 9% 23% 39% 8% 11% 20% 32% 5% 6% 15% 23% 4% Katowice 2% 10% 27% 6% 5% 16% 30% 5% 10% 18% 28% 5% 6% 16% 27% 5% Kielce 0% 14% 33% 7% 5% 19% 31% 6% 11% 21% 33% 5% 6% 16% 30% 5% Koszalin 1% 11% 29% 6% 7% 16% 34% 5% 9% 17% 28% 5% 6% 15% 23% 4% Kraków 2% 12% 28% 6% 6% 19% 35% 6% 9% 20% 33% 6% 6% 16% 25% 5% Lublin 4% 16% 34% 7% 11% 22% 35% 6% 10% 20% 34% 5% 6% 15% 24% 4% Łódź 3% 15% 31% 7% 6% 21% 31% 6% 9% 22% 31% 5% 5% 16% 28% 5% Olsztyn 1% 12% 27% 6% 6% 20% 39% 7% 9% 19% 28% 5% 5% 15% 26% 4% Opole 3% 15% 31% 7% 8% 21% 40% 7% 8% 20% 32% 6% 7% 14% 27% 5% Poznań 6% 18% 36% 9% 13% 25% 37% 6% 11% 22% 34% 5% 2% 14% 25% 6% Rzeszów 1% 13% 33% 7% 9% 21% 44% 7% 9% 20% 36% 6% 6% 14% 25% 5% Suwałki 2% 13% 25% 6% 5% 21% 39% 6% 6% 19% 30% 6% 8% 16% 26% 4% Szczecin 2% 16% 41% 8% 8% 21% 34% 6% 9% 21% 36% 6% 7% 15% 25% 4% The annual fraction with 20-day cumulative rainfalls according to the class intervals of [0-10) mm, [10][11][12][13][14][15][16][17][18][19][20] mm, [20][21][22][23][24][25][26][27][28][29][30] mm, and [30][31][32][33][34][35][36][37][38][39][40] mm was calculated and summarised in Table 3. The annual average frequency of periods with a 20-day cumulative rain between [0-10) mm ranged from 10% for Katowice to 21% for Gdańsk.…”

“…The annual average frequency of periods with a 20-day cumulative rain between [0-10) mm ranged from 10% for Katowice to 21% for Gdańsk. In the case of the interval between [10][11][12][13][14][15][16][17][18][19][20] mm, the smallest average found was 16% (Katowice and Koszalin), while a highest equal to 25% found in three cities: Gdańsk, Poznań and Toruń. For the interval between [20][21][22][23][24][25][26][27][28][29][30] mm, the average fraction of the year ranged from 17% (Koszalin) to 22% (Łódź and Poznań).…”

“…To increase the readability of the table, statistically significant changes ( ≥ 95%), changes close to statistical significance ( from 90 to 95%) and tendencies to change ( from 75 to 90%) are highlighted blue (increasing) and yellow (decreasing). There is evidence of statistically significant upward trends for Gorzów Wielkopolski ( [30][31][32][33][34][35][36][37][38][39][40] It is worth noting that for Poznań the amount of 20-day rainfall sums in the ranges [0-10) mm (CLI = 68%) and [10][11][12][13][14][15][16][17][18][19][20] mm (CLI = 91%) decreased, while there was no increase in the ranges [20][21][22][23][24][25][26][27][28][29][30] mm and [30][31][32][33][34][35][36][37][38][39][40] mm. However, let us observe (Table 4) that Poznań is the only city in which a clear upward tre...…”

“…In water supply systems, one of the main objectives is reducing the water losses by preventing failures in water intakes and networks. Consequently, integrated water management systems employ the support of advanced computer models and artificial neural networks to achieve this goal [13][14][15]. The rainwater harvesting (RWH) is promoted as a widely available, alternative source of water for an entire range of uses, including household purposes, and its implementation in residential buildings are regarded as economically and ecologically beneficial, as long as adequate maintenance and operation are guaranteed [16].…”