Local scour is an of import issue in environmental scientific discipline and technology in order to forestall debasement of river bed and safe the stableness of grade control structures-stilling basins, aprons, ski-jump pail wasteweirs, bed Sillss, weirs, cheque dikes, etc. This survey presents Gene-Expression Programming ( GEP ) which is an extension to Genetic Programming ( GP ) as an alternate attack to foretell scour deepness downstream of Sillss. Published informations were compiled from the literature for the scour deepness downstream of Sillss. The proposed GEP attack produce satisfactory consequences compared ( R2=0.967 and RMSE =0.088 ) to bing forecasters for scour deepness.

Local scour modeling is an of import issue in environmental technology in order to forestall debasement of river bed and safe the stableness of class control structures ( Laucelli and Giustolisi, 2010 ) . In an estuary or a river, a sill may be the initial foundation or the lower portion of construction that has to be constructed on a bed of alluvial stuff. The bed in the direct vicinity of hydraulic construction is by and large protected against current, moving ridges, and Eddies ( Hoffman and Verheij, 1997 ) . The length of the bed protection depends on the allowable scour deepness. Local scour is the eroding of bed surface and the hydraulic constructions due to the impact consequence of fluxing H2O. Grade-control constructions are built in order to forestall inordinate channel-bed debasement in alluvial channels. However, local scour downstream of grade-control constructions occurs due to erosive action of the weir flood and this action may sabotage these constructions ( Bormann and Julien, 1991 ) . Hydraulic grade-control constructions have been widely used to increase incline stableness and command scour in mountain watercourses ( Chinnarasri and Kositgittiwong, 2008 ) . They are built across the rivers in low-stability countries, or in countries that have to be adjusted from steeper inclines to less terrible inclines ( Gaudio, et al 2000 ; Lenzi et al. , 2002 ; and Marion et al. , 2004 ) .

Most of the old research workers focused on local scouring at stray bead constructions by free jets through experimental surveies ( Volkart et al 1973 and Whittakar, 1987 ) Summaries of research for the job of individual, stray bead constructions can be found in Lenzi et Al. ( 2002 ) Owing to the complexness of flow features, such as flow deepness, sills spacing, tallness of H2O jet and clip development, much less is known about the instance of a staircase-like sequence of class control structures ( Gaudio and Marion, 2003 ; Lenzi et al. , 2003 ; and Lenzi and Comiti, 2003 ) . The rule of grade-control constructions is to diminish bed incline by spliting it into dividers. Initial steep bed incline is scoured greatly, but when there are grade-control constructions, longitudinal channel incline is decreased to a lower value called an ultimate incline, stand foring a dynamic equilibrium between bed scouring and aggradation ( Lenzi et al. , 2003 ; and Lenzi and Comiti, 2003 ) .

The procedures of debasement halt and bed profile are stabilised. Under the same flow and sediment rates, the bed slopes between Sillss are found to be less terrible than without Sillss: a consequence which corresponds to the instance of clear H2O. Less terrible inclines, in comparing with the initial incline, show the possible debasement prevented by the Sillss ( Martin-Vide and Andreatt, 2006 ; Marion et al. , 2006 ) .

The parametric quantities concerned with the i¬‚ow and local scouring downstream of bed Sillss may dwell of critical specii¬?c energy ( Hs ) , maximal deepness of the scour hole at the equilibrium status ( Y ) , initial bed incline So, equilibrium bed incline ( Seq ) , sill spacing ( L ) , average deposit size D50, denseness of H2O I?w, submerged denseness of deposit I?s, screening index ( SI ) and acceleration due to gravitation ( g ) , as shown in Fig. 1 ( Chinnarasri and Kositgittiwong, 2008 ) . The consequence of deposit sorting can be described by a mention size, D50, and a geometric criterion divergence, I?g, of the atoms. The screening index

was proposed by ( Chinnarasri and Kositgittiwong, 2008 ) , and morphological leap a= ( S0-Seq ) L which equivalent to head bead ( Gaudio et al, 2000 ) . Scour can be expressed as

( 1 )

A dimensional analysis Eq. ( 1 ) can be reduced to a set of six non-dimensional parametric quantities, it gives

( 2 )

where a?†= ( I?s-I?w ) /I?w is the comparative submersed denseness of deposit. Lenzi et Al. ( 2002 ) carried out local scouring surveies in high gradient watercourses where the initial bed inclines were 0.0785 m/m, 0.1145 m/m and 0.1480 m/m, severally. They found that the maximal scour deepness on low- and high-gradient watercourses can be expressed with the non-linear equation as ( valid for 0.16a‰¤a/a?†D95a‰¤ 1.15 )

( 3 )

During the last two decennaries, research workers were chiefly utilizing soft calculating techniques for controlled research lab informations, and the consequences were demonstrated to be significantly better than those from conventional statistical methods ( Giustolisi, 2004 ; Azmathulla et al. , 2010 ) . Use of unreal nervous webs ( ANN ) to foretell the scour around and downstream of hydraulic constructions, was reported by Azmathullah et Al. ( 2005 ) . However, utilizing ANNs as a mere black-box to reproduce an input-output sequence good does non assist in progressing the scientific apprehension of hydraulic procedures so non attempted in the present survey. Recently, gene-expression scheduling ( GEP ) has attracted attending in the anticipation of hydraulic features ; yet its usage for hydraulic applications is limited, and needs farther geographic expedition. This survey presents a new soft calculating GEP as alternate tool for gauging scour downstream of Sillss.

## Overview of GEP

GEP, which is an extension of GP ( Koza, 1992 ) , is a hunt technique that involves computing machine plans ( e.g. , mathematical looks, determination trees, multinomial concepts, and logical looks ) . GEP computing machine plans are all encoded in additive chromosomes, which are so expressed or translated into look trees ( ETs ) . ETs are sophisticated computing machine plans that have normally evolved to work out a peculiar job and are selected harmonizing to their fittingness at work outing that job.

GEP is a fully fledged genotype/phenotype system, with the genotype wholly separated from the phenotype, whereas in GP, genotype and phenotype are assorted together in a simple replicator system. As a consequence, the fully fledged genotype/phenotype system of GEP surpasses the old GP system by a factor of 100-60,000 ( Ferreira 2001a, B ) .

Initially, the chromosomes of each person in the population are generated indiscriminately. Then, the chromosomes are expressed, and each person is evaluated based on a fittingness map and selected to reproduce with alteration, go forthing offspring with new traits. The persons in the new coevals are, in their bend, subjected to some developmental procedures, such as look of the genomes, confrontation of the choice environment, and reproduction with alteration. These procedures are repeated for a predefined figure of coevalss or until a solution is achieved ( Ferreira 2001a, B ) . The functionality of each familial operator included in GEP system has been explained by Guven and Aytek ( 2009 ) .

## Derivation of Froude Number based on GEP

In this subdivision, the deposit burden is modeled utilizing the GEP attack. Initially, the “ preparation set ” is selected from the full information set, and the remainder is used as the “ testing set ” . Once the preparation set is selected, one could state that the larning environment of the system is defined. The mold besides includes five major stairss to fix to utilize GEP. The first is to take the fittingness map. For this job, the fittingness, fi, of an single plan, I, is measured by:

( 4 )

where M is the scope of choice, C ( I, J ) is the value returned by the single chromosome I for fittingness instance J ( out of Ct fittingness instances ) and Tj is the mark value for fittingness instance J. If |C ( one, J ) – Tj| ( the preciseness ) a‰¦ 0.01, so the preciseness is 0, and fi = fmax = CtM. In this instance, M = 100 is used ; hence, fmax = 1000. The advantage of this sort of fittingness map is that the system can happen the optimum solution by itself.

Second, the set of terminuss T and the set of maps F are chosen to make the chromosomes. In this job, the terminus set consists of individual independent variable, i.e. , T = { H } . The pick of the appropriate map set is non so clear ; nevertheless, a good conjecture is helpful if it includes all the necessary maps. In this survey, four basic arithmetic operators ( + , – , * , / ) and some basic mathematical maps ( a?s ) are utilised.

The 3rd major measure is to take the chromosomal architecture, i.e. , the length of the caput and the figure of cistrons. We ab initio used individual cistron and two caput lengths and increased the figure of cistrons and caputs one at a clip during each tally while we monitored the preparation and proving public presentations of each theoretical account. We observed that more than two cistrons more and a caput length greater than 8 did non significantly better the preparation and proving public presentation of GEP theoretical accounts. Therefore, the caput length, lh = 8, and two cistrons per chromosome are employed for each GEP theoretical account in this survey.

The 4th major measure is to take the linking map. In this survey, add-on and generation operators are used as associating maps, and it is observed that associating the sub-ETs by add-on gives better fittingness ( Eq. 4 ) values. The fifth and concluding measure is to take the set of familial operators that cause fluctuation and their rates. A combination of all familial operators ( mutant, heterotaxy and crossing over ) is used for this intent ( Table 2 ) .

Table 3 compares the GEP theoretical account with one of the independent parametric quantities removed in each instance and any independent parametric quantity from the input set that yielded larger RMSE and lower R2 values besides removed. These five independent parametric quantities affect ; therefore, the functional relationship given in Eq. ( 1 ) is used for the GEP theoretical account in this survey. The GEP attack resulted in a extremely nonlinear relationship between and the input parametric quantities, and the GEP theoretical account had the highest truth and the lowest mistake ( Table 3 ) .

The GEP theoretical account was calibrated with 105 input-target braces of collected informations ( Table 1 ) . Among the 105 informations sets, 25 ( 25 % ) were reserved for proof ( proving ) , and the staying 80 sets were used to graduate the GEP theoretical account.

The best single in each coevals has 30 chromosomes has and a fittingness 555.6 for. The expressed preparations of GEP for are given in Eq. ( 5 ) , and the corresponding look trees are shown in Fig. 4.

## +

( 5 )

## Training and proving consequences of GEP patterning

The public presentation of GEP in preparation and proving sets is evaluated in footings of four common statistical steps such as R2 ( coefficient of finding ) , RMSE ( root mean square mistake ) , MAE ( average norm mistake ) and vitamin D ( mean absolute divergence ) which are expressed as follows:

( 6 )

( 7 )

where denotes the mark values of, while and denotes the ascertained and averaged ascertained values of, severally, and N is the figure of informations points. The scope of fluctuation of collected information for this survey, and its parametric quantities are shown in Table 1. The functional set and operational parametric quantities used in the present GEP mold are listed in Table 2.

## Consequences and treatment

The consequences of the GEP theoretical account and Chinnarasri and Kositgittiwong ( 2008 ) equation are computed utilizing the collected information set and are compared with the measured informations. It is observed that, the GEP has good consequence and there are considerable mistakes in comparing with the measured information. This indicates the hapless public presentation of empirical equation proposed by Chinnarasri and Kositgittiwong ( 2008 ) for the anticipation of scour downstream of Sillss. From Figure 2 it is clear that there is significant spread between observed and predicted comparative scour deepness. The GEP theoretical account predicted reasonably accurate and comparable ( R2=0.967 and RMSE =0.088 ) with the old research workers. With the promotions in computing machine hardware and package, the application of soft-computing tools should non present jobs in even everyday applications. The advantage of the GEP technique is that it is easy to cover with physical anterior cognition possibly because it works in a similar manner as worlds, particularly when applied to field informations from the rivers, to execute scientific find, as in this work.

## Decisions

A gene-expression scheduling attack is used to deduce a new look for the anticipation of scour downstream of Sillss. The proposed equation can be used to gauge scour deepness for Mountain Rivers for assorted bed inclines. Performance of the GEP look is carried out by comparing its anticipations with the published informations ( R2=0.967 and RMSE =0.088 ) . The comparing shows that the new look has the least root average square mistake and the highest coefficient of finding. The look is found to be peculiarly suited for bed inclines where anticipations are really near to the measured scour deepness