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Pests and Diseases Forewarning System. Amrender Kumar. Scientist Indian Agricultural Statistics Research Institute, Library Avenue, New Delhi, INDIA [email protected] Crop – Pests - Weather Relationship. Crop. Weather. Pests.

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Pests and Diseases Forewarning System

Amrender Kumar

Scientist

Indian Agricultural Statistics Research Institute,

Library Avenue, New Delhi, INDIA

[email protected]


Crop – Pests - Weather

Relationship

Crop

Weather

Pests


  • Diseases and pests are major causes of reduction in crop yields.

  • However, in case information about time and severity of outbreak of diseases and pests is available in advance, timely control measures can be taken up so as to reduce the losses.

  • Weather plays an important role in pest and disease development.

  • Therefore, weather based models can be an effective scientific tool for forewarning diseases and pests in advance.


Why pests and disease forewarning
Why pests and disease forewarning yields.

  • Forewarning / assessment of disease important for crop production management

    • for timely plant protection measures

      • information whether the disease status is expected to be below or above the threshold level is enough, models based on qualitative data can be used – qualitative models

    • loss assessment

      • forewarning actual intensity is required - quantitative model


Variables of interest
Variables of interest yields.

  • Maximum pest population or disease severity.

  • Pests population/diseases severity at most damaging stage i.e. egg, larva, pupa, adult.

  • Pests population or diseases severity at different stages of crop growth or at various standard weeks.

  • Time of first appearance of pests and diseases.

  • Time of maximum population/severity of pests and diseases.

  • Weekly monitoring of pests and diseases progress.

  • Occurrence/non-occurrence of pests & diseases.

  • Extent of damage.


Data structure
Data Structure yields.

Historical data at periodical intervals for 10-15 years



  • Data for 5-6 years at periodic intervals yields.

    • For week-wise models, data points inadequate

    • combined model for the whole data in two steps

  • Data at one point of time for 5-6 years

    • Model development not possible

  • Qualitative data for 10-15 years

    • Qualitative forewarning

      • Occurrence / non-occurrence of disease

  • Mixed data – conversion to qualitative categories

  • Data collected at periodic intervals for one year

    • Within year growth model


Choice of explanatory variables yields.

  • Relevant weather variables

    • appropriate lag periods depending on life cycle

  • Crop stage / age

  • Natural enemies

  • Starting / previous year’s last population of pathogen


Forecast models
Forecast Models yields.

  • Between year models

    • These models are developed using previous years’ data.

    • The forecast for pests and diseases can be obtained by substituting the current year data into a model developed upon the previous years.

  • Within year models

    • Sometimes, past data are not available but the pests and diseases status at different points of time during the current crop season are available.

    • In such situations, within years growth model can be used, provided there are 10-12 data points between time of first appearance of pests and diseases and maximum or most damaging stage.

    • The methodology consists of fitting appropriate growth pattern to the pests and diseases data based on partial data.


Thumb rules yields.

  • Most common

  • Extensively used

  • Judgment based on past experience with no or little mathematical background

    Example

    A day is potato late blight favorable if

  • the last 5 - day temperature average is < 25.50 C

  • the total rainfall for the last 10 days is > 3.0 cm

  • the minimum temperature on that day is > 7.20 C

    Trivedi et al. (1999)


  • Regression models yields.

    • Relationship between two or more quantitative variables

    • The model is of the form

      Y = 0 + 1 X1+2 X2 ………. +p Xp + e ,

      where

      • i’s are regression coefficients

      • Xi’s are independent variables

      • Y variable to forecast

      • e random error

    • Variables could be taken as such or some suitable transformations


    Cotton yields.

    • % ofincidence of Bacterial blight (Akola) – Weekly models (42nd to 44th SMW)

    • Data used: 1993-1999 on MAXTemp, MINTemp, RH1 (morn), RH2 (aft) and RF – [X1 to X5) lagged by 2 to 4 weeks

    • Model for 44th SMW

      Y= 133.18 - 3.09 RH2L4 + 1.68 RFL4 (R2=0.78)


    Potato yields.

    • Potato aphid is an abundant potato pest and vector of potato leaf-roll virus, potato virus Y , PVA, etc.

    • Potato aphid population – Pantnagar (weekly models)

    • Data used: 1974-96 on MAXT, MINT and RH

      – [X1 to X3) lagged by 2 weeks

    • Model for December 3rd week

      Y = 80.25 + 40.25 cos (2.70 X12 - 14.82)

      + 35.78 cos (6.81 X22 + 8.03)



    Gdd approach

    GDD = yields. (mean temperature – base temperature)

    The decision of

    Base temperature

    Initial time

    Not much work on base temperature for various diseases

    Normally base temperature is taken as 50 C

    Under Indian conditions, mean temperature is seldom below 50 C

    Use of GDD and simple accumulation of mean temperature will provide similar results in statistical models

    Need for work on base temperature and initial time of calculation

    GDD approach


    where


    Y variable to forecast yields.

    xiw value of ith weather variable in wth period

    riw weight given to i-th weather variable in wth period

    rii’w weight given to product of xi and xi’ in wth period

    p number of weather variables

    n1 and n2 are the initial and final periods for which weather

    variables are to be included in the model

    e error term


    Experience based weights yields.

    • Subjective weights based on experience.

      • Weather variable not favourable : weight = 0

      • Weather variable favourable : weight = ½

      • Weather variable very favourable : weight = 1


    • Example : yields.

    • Favourable relative humidity  92%

    • Most favourable relative humidity  98%

    • Weather data

    • Year Week No.

    • 1 2 3 4 5 6

    • 1993 88.7 90.1 94.4 98.3 98.0 95.0

    • 94.0 93.3 94.9 93.3 92.0 88.1

    • 90.3 91.9 90.4 87.9 86.4 89.7

    • ----------------------------------------------------------------

    • ----------------------------------------------------------------


    • Weighted Index yields.

    • 0x 88.7 + 0x90.1 + 0.5 x 94.4 + 1 x 98.3 +

    • 1 x 98 + 0.5 x 95 = 271.0

    • 0.5 x 94 + 0.5 x 93.3 + 0.5 x 94.9 +

    • 0.5 x 93.3 + 0.5 x 92 + 0 x 88.1 = 232.6

    • 0 x 90.3 + 0 x 91.9 + 0 x 90.4 + 0x 87.9 +

    • 0 x 86.4 + 0 x 89.7 = 0.0

    • ---------------------------------------------------------------

    • ----------------------------------------------------------------


    Interaction yields. :

    Both variables not favourable : weight = 0

    One variable not favourable, one variable favourable : weight = 1/8

    One variable not favourable, one variable highly favourable : weight = ¼

    Both variables favourable : weight = ½

    One variable favourable, one variable highly favourable : weight = ¾

    Both variables highly favourable : weight = 1


    Correlation based weights yields.

    riw correlation coefficient between Y and i-th weather

    variable in wth period

    rii’w correlation coefficient between Y and product of xi and xi’

    in wth period


    • Modified model yields.

    • Model using both weighted and unweighted indices

    where


  • The first indexrepresents total amount of weather variable received by the crop during the period under consideration

  • The other onetakes care of distribution of weather variable with reference to its importance in different periods in relation to variable to forecast

  • On similar lines, composite indices were computed with products of weather variables (taken two at a time) for joint effects.


  • Pigeon pea
    Pigeon pea developed

    Phytophthora blight (Kanpur)

    • Average percent incidence of phytophthora blight at one point of time

    • Data used : 1985-86 to 1999-2000 on MAXT, MINT, RH1, RH2 and RF (X1- X5) from 28th to 33rd SMW

      Y = 330.77 + 0.12 Z121 ….. (R2 = 0.77)


    Sterility Mosaic developed

    • Average percent incidence of sterility mosaic

    • Data used : 1983-84 to 1999-2000 for MAXT, MINT, RH1, RH2 and RF (X1- X5) from 20th to 32nd SMW

      Y = -180.41 + 0.09 Z121 …… (R2 = 0.84)



    Groundnut
    Groundnut developed

    Late Leaf Spot & Rust – Tirupathi

    • Disease indices at one point of time

    • Data used : MAXT, MINT, RH1, RH2, RF and WS from (X1- X6)

      - 10th to 14th SMW (Rabi or post rainy)

      - 41st to 46th SMW (Kharif or rainy)



    Principal component regression (Tirupati)

    • Independent variables large and correlated

    • Independent variables transformed to principal components

    • First few principal components explaining desired variation selected

    • Regression model using principal components as regressors


    Discriminant function analysis (Tirupati)

    • Based on disease status years grouped into different categories – low, medium, high

    • Linear / quadratic discriminant function using weather data in above categories

    • Discriminant score of weather for each year

    • Regression model using disease data as dependent variable and discriminant scores of weather as independent.

    • Data requirement is more.

    • Can also be used if disease data are qualitative

    • Johnson et al. (1996) used discriminant analysis for forecasting potato late blight.


    Deviation method (Tirupati)

    • Useful when only 5-6 year data available for different periods

    • Week-wise data not adequate for modeling

    • Combined model considering complete data.

    • Not used for disease forewarning but in pest forewarning


    • Assumption : pest population / disease incidence in particular year at a given point of time composed of two components.

      • Natural growth pattern

      • Weather fluctuations

    • Natural pattern to be identified using data in different periods averaged over years.

    • Deviation of individual years in different periods from predicted natural pattern to be related with deviations of weather.


    Mango particular year at a given point of time composed of two components.

    • Mango fruitfly – Lucknow (weekly models)

    • Data used: 1993-94 to 1998-99 on MAXT, MINT and RH – [X1 to X3]

    • Model for natural pattern

    t = Week no.

    Yt = Fruitfly population count at week t


    Forecast model
    Forecast model particular year at a given point of time composed of two components.

    Y =  125.766 + 0.665 (Y2) + 0.115 (1/X222 ) + 10.658 (X212)

    + 0.0013 (Y23) + 31.788 (1/Y3)  21.317 (X12)

     2.149 (1/X233)  1.746 (1/X234)

    Y = Deviation of fruitfly population from natural cycle

    Yi = Fruitfly population in i-th lag week

    Xij = Deviation from average of i-th weather variable (i =

    1,2,3 corresponds to maximum temperature,

    minimum temperature and relative humidity) in j-th lag

    week.


    Soft Computing Techniques particular year at a given point of time composed of two components.


    With the development of computer hardware and software and the rapid computerization of business, huge amount of data have been collected and stored in centralized or distributed databases

    Data is heterogeneous (mixture of text, symbolic, numeric, texture, image), huge (both in dimension and size) and scattered.

    The rate at which such data is stored is growing at a phenomenal rate.

    As a result, traditional statistical techniques and data management tools are no longer adequate for analyzing this vast collection of data.


    • One of the applications of Information Technology that has drawn the attention of researchers is data mining, where pattern recognition, image processing, machine intelligence i.e concerned with the development of algorithms and techniques that allow system to "learn“ are directly related

    • Data Mining involves

      • Statistics : Provides the background for the algorithms.

      • Artificial Intelligence : Provides the required heuristics for learning the system

      • Data Management : Provides the platform for storage & retrieval of raw and summary data.


    Pattern Recognition drawn the attention of researchers is data mining and Machine Learning principles applied to a very large (both in size and dimension) heterogeneous database for Knowledge Discovery

    Knowledge Discovery is the process of identifying valid, novel, potentially useful and ultimately understandable patterns in data. Patterns may embrace associations, correlations, trends, anomalies, statistically significant structures etc.

    Without “Soft Computing” Machine Intelligence and Data Mining may remains Incomplete


    Soft computing
    Soft Computing drawn the attention of researchers is data mining

    Soft Computing is a new multidisciplinary field that was proposed by Dr.LotfiZadeh, whose goal was to construct new generation Artificial Intelligence, known as Computational Intelligence.

    The concept of Soft Computing has evolved. Dr.Zadeh defined Soft Computing in its latest incarnation as the fusion of the fields of fuzzy logic, neural network, neuro-computing, Evolutionary & Genetic Computing and Probabilistic Computing into one multidisciplinary system.

    Soft Computing is the fusion of methodologies that were designed to model and enable solutions to real world problems, which are not modeled, or too difficult to model. These problems are typically associated with fuzzy, complex, and dynamical systems, with uncertain parameters.

    These systems are the ones that model the real world and are of most interest to the modern science.


    The main goal of Soft Computing is to develop intelligent system and to solve nonlinear and mathematically unmodelled system problems [Zadeh 1993, 1996, and 1999].

    The applications of Soft Computing have two main advantages.

    First, it made solving nonlinear problems, in which mathematical models are not available, possible.

    Second, it introduced the human knowledge such as cognition, recognition, understanding, learning, and others into the fields of computing.

    This resulted in the possibility of constructing intelligent systems such as autonomous self-tuning systems, and automated designed systems.


    Soft computing tools
    soft computing tools system and to solve nonlinear and mathematically unmodelled system problems [Zadeh 1993, 1996, and 1999].

    Soft computing tools include

    • Fuzzy sets

      • Fuzzy sets provide a natural frame work for the process in dealing with uncertainty

    • Artificial neural networks

      • Neural networks are widely used for modelling complex functions and provide learning and generalization capabilities

    • Genetic algorithms

    • Genetic algorithms are an efficient search and optimization tool

  • Rough set theory

    • Rough sets help in granular computation and knowledge discovery


  • Why Neural Networks are desirable system and to solve nonlinear and mathematically unmodelled system problems [Zadeh 1993, 1996, and 1999].

    Human brain can generalize from abstract

    Recognize patterns in the presence of noise

    Recall memories

    Make decisions for current problems based on prior experience

    Why Desirable in Statistics

    Prediction of future events based on past experience

    Able to classify patterns in memory

    Predict latent variables that are not easily measured

    Non-linear regression problems


    Application of anns
    Application of ANNs system and to solve nonlinear and mathematically unmodelled system problems [Zadeh 1993, 1996, and 1999].

    Classification:

    medical diagnosis

    signature verification

    character recognition

    voice recognition

    image recognition

    face recognition

    loan risk evaluation

    data mining

    Modelling and Control

    control systems

    system identification

    composing music

    Forecasting:

    economic indicators

    energy requirements

    medical outcomes

    crop forecasts

    environmental risks


    Neural networks are being successfully applied across an extraordinary range of problem domains, in areas as diverse as finance, medicine, engineering, geology, biology, physics and agriculture.

    From a statistical perspective neural networks are interesting because of their potential use in prediction and classification problems.

    A very important feature of these networks is their adaptive nature, where “Learning by Example” replaces “Programming” in solving problems.

    Basic capability of neural networks is to learn patterns from examples


    Type of neural network models extraordinary range of problem domains, in areas as diverse as finance, medicine, engineering, geology, biology, physics and agriculture.

    Two types of neural network models

    Multilayer perceptron (MLP) with different hidden layers and nodes

    Radial basis function (RBF)


    Neural network based model
    Neural network based model extraordinary range of problem domains, in areas as diverse as finance, medicine, engineering, geology, biology, physics and agriculture.

    Steps in developing a neural network model

    Forming training, testing and validation sets

    Neural network model

    No. of input nodes

    No. of hidden layers

    No. of hidden nodes

    No. of output nodes

    Activation function

    Model building

    Sensitivity Analysis


    Data sets
    Data sets extraordinary range of problem domains, in areas as diverse as finance, medicine, engineering, geology, biology, physics and agriculture.

    The data available is divided into three data sets

    Training set represents the input- output mapping, which is used to modify the weights.

    Validation set is required only to decide when to stop training the network, and not for weight update.

    Test set is the part of collected data that is set aside to test how well a trained neural network generalizes.


    No. of input nodes : more than one extraordinary range of problem domains, in areas as diverse as finance, medicine, engineering, geology, biology, physics and agriculture.

    No. of hidden layers : one / two

    No. of hidden nodes : decided by various rules

    No. of output nodes : one

    Activation function : hyperbolic


    Activation function: extraordinary range of problem domains, in areas as diverse as finance, medicine, engineering, geology, biology, physics and agriculture.

    Activation functions determine the output of a processing node. Non linear functions have been used as activation functions such as logistic, tanh etc.

    Activation functions such as sigmoid are commonly used because they are nonlinear and continuously differentiable which are desirable for network learning

    Logistic activation functions are mainly used for classification problems which involve learning about average behavior

    Hyperbolic tangent functions are used for the problem involves learning about deviations from the average such as the forecasting problem.

    Therefore, in the present study, hyperbolic tangent (tanh) function has been used as activation function for neural networks model based on MLP architecture.


    Input extraordinary range of problem domains, in areas as diverse as finance, medicine, engineering, geology, biology, physics and agriculture.

    Output


    Learning of anns
    Learning of ANNs extraordinary range of problem domains, in areas as diverse as finance, medicine, engineering, geology, biology, physics and agriculture.

    The most significant property of a neural network is that it can learn from environment, and can improve its performance through learning

    Learning is the process of modifying the weights in networks

    The network becomes more knowledgeable about environment after each iteration of learning process.

    There are mainly two types of learning paradigms

    Supervised learning

    Unsupervised learning


    A learning cycle in the mlp backpropagation learning algorithm
    A learning cycle in the MLP extraordinary range of problem domains, in areas as diverse as finance, medicine, engineering, geology, biology, physics and agriculture. (Backpropagation Learning Algorithm)

    Output vector

    Target vector

    Differences

    Input vector

    ANN model

    =

    Adjust weights


    Mustard extraordinary range of problem domains, in areas as diverse as finance, medicine, engineering, geology, biology, physics and agriculture.

    Alternaria blight (Varuna, Rohini & Binoy)

    Bharatpur (Raj)

    Behrampur (WB)

    Dholi (Bihar)

    Powdery mildew (Varuna and GM2)

    S.K.Nagar

    Variable to forewarn

    crop age at first appearance of disease

    crop age at peak severity of disease

    maximum severity of disease

    Cotton

    Bacterial blight (% of disease incidence) - Akola


    Pests diseases forewarning mustard
    Pests / diseases forewarning- extraordinary range of problem domains, in areas as diverse as finance, medicine, engineering, geology, biology, physics and agriculture. Mustard

    Data have been taken from Mission Mode Project under National Agricultural Technology Project, entitled “Development of weather based forewarning system for crop pests and diseases”, at CRIDA, Hyderabad.

    Models were developed for forecasting different aspects relating to diseases for Alternaria Blight (AB) and Powdery Mildew (PM) in Mustard crop.

    The field trials were sown on 10 dates at weekly intervals (01, 08, 15, 22, 29 October, 05, 12, 19, 26 November and 03 December) at each of the locations viz., Bharatpur, Dholi and Berhampur for Alternaria Blight and at S.K.Nagar for Powdery Mildew.

    Data for different dates of sowing were taken together for model development.

    Weekly data on weather variables starting from week of sowing up to six weeks of crop growth were considered

    Forewarning models were developed for two varieties of mustard crop for

    Alternaria Blight on leaf and pod (Varuna and Rohini – Bharatpur, Varuna and Binoy – Behrampur and Varuna and Pusabold – Dholi) and

    Powdery Mildew on leaf (Varuna and GM2 – S.K.Nagar)

    Models have been validated using data on subsequent years not included in developing the models.


    Mean Absolute Percentage Error of various models at extraordinary range of problem domains, in areas as diverse as finance, medicine, engineering, geology, biology, physics and agriculture. Bharatpur in different varieties in mustard crop for Alternaria blight (AB) - 2006-07


    Neural networks, with their remarkable ability to derive meaning from complicated or imprecise data, can be used to extract patterns and classifications

    Neural networks do not perform miracles. But if used sensibly they can produce some amazing results


    Model for qualitative data meaning from complicated or imprecise data, can be used to extract patterns and classifications

    • Data in categories

    • Occurrence / non-occurrence, low / medium / high, etc.

    • Classified as 0 / 1 (2 categories); 0,1,2 (three categories)

    • Quantitative data / mixed data can be converted to categories


    Logistic Regression model meaning from complicated or imprecise data, can be used to extract patterns and classifications

    • where, L= β0+ β1x1+ β2x2 ….βnxn

    • x1 , x2, x3,…xn are weather variables/weather indices

    • e = random error

    • Forecast / Prediction rule

      • If P < 0.5, then the probability of epidemic occurrence will be minimal

      • If P  0.5, then there is more chance of occurrence of epidemic.


    Rice meaning from complicated or imprecise data, can be used to extract patterns and classifications

    • Leaf blast severity (%) - Palampur at one point of time

    • Data used: 1991-92 to 1998-99 on MAXT, MINT, RH1, RH2, BSH & RF – [X1 to X6] from 23th to 31st SMW.

    • Model :

      L= 394.8 -0.0520 Z351-1.5414 Z10

    • Validation for subsequent years :


    Mustard
    Mustard meaning from complicated or imprecise data, can be used to extract patterns and classifications

    Alternaria blight and White rust

    • Data used: 1987-88 to 1998-99 on MAXT, MINT, RH1, RH2 and BSH – (X1 to X5) from week of sowing (n1) to 50th smw (n2)

      Model forAlternaria blight

      L =- 8.8347 + 0.0163 Z120 - 0.00037 Z130 - 0.00472 Z450

      Model for White rust

      L = 5.8570 - 0.0293Z40 + 0.00264 Z230

    • Forecasts of subsequent years are


    Within year model meaning from complicated or imprecise data, can be used to extract patterns and classifications

    • Model using only one year’s data

      • Data availability for several dates of sowing

      • If adequate dates of sowing, models similar to between-year models could be developed

    • Use for forewarning subsequent years (?)

    • Model for single date of sowing

      • Forewarning of maximum disease severity

      • Applicable when 10-12 data observations between first disease appearance and maximum disease severity

      • Non-linear model for disease development pattern growth using partial data


    • Mustard meaning from complicated or imprecise data, can be used to extract patterns and classifications

    • Alternaria blight cv. Varuna (% disease severity) - Kumarganj

    • Data used: 1999-2000

    • Model :

    • Yt = A exp (B/t)

    • Yt = pds at time t, A and B are parameters,

    • t = week after sowing (1,2,…….)


    Observed, predicted and forecasts of max. percent disease severity (PDS)

    • Reliable forecast of max. pds could be obtained for 2 weeks in advance


    Models developed at iasri
    Models developed at IASRI severity (PDS)

    • Sugarcane

      • Pyrilla

      • Early shoot borer &

      • Top borer

    • Pigeon pea

      • Pod fly

      • Pod borer

      • Sterility Mosaic

      • Phytophthora Blight

    • Rice

      • BPH

      • Gall midge

    • Mango

      • Powdery Mildew

      • hoppers

      • fruit-fly

    • Mustard

      • Alternaria Blight

      • White Rust

      • Powdery Mildew

      • Aphid

    • Cotton

      • American boll worm

      • Pink boll worm

      • Spotted boll worm

      • Whitefly

    • Groundnut

      • Spodoptera litura

      • Late leaf blast

      • Rust

    • Onion

      • Thrips


    References
    References severity (PDS)

    • Agrawal, Ranjana, Jain, R.C. and Jha, M.P. (1983). Joint effects of weather variables on rice yields. Mausam, 34(2), 177-81.

    • Agrawal, Ranjana, Jain, R.C., Jha, M.P., (1986). Models for studying rice crop weather relationship, Mausam, 37(1), 67-70.

    • Agrawal Ranjana, Mehta, S.C., Kumar, Amrender and Bhar, L.M. (2004). Development of weather based forewarning system for crop pests and diseases- Report from IASRI, Mission mode project under NATP, PI, Dr. Y.S. Ramakrishna, CRIDA, Hyderabad.

    • Denton, J.W., 1995. How good are neural networks for causal forecasting? Journal of Business Forecasting, 14 (2), 17–20.

    • Desai, A.G., Chattopadhyay, C., Agrawal, Ranjana, Kumar, A., Meena, R.L., Meena, P.D., Sharma, K.C., Rao, M. Srinivasa, Prasad,, Y.G. and Ramakrishna, Y.S. (2004). Brassica juncea powdery mildew epidemiology and weather-based forecasting models for India - a case study , Journal of Plant Diseases and Protection, 111(5), 429-438.

    • Gaudart, J., Giusiano, B. and Huiart, L. (2004). Comparison of the performance of multi-layer perceptron and linear regression for epidemiological data. Comput. Statist. & Data Anal., 44, 547-70.


    • Hebb, D.O. (1949) The severity (PDS)organization of behaviour: A Neuropsychological Theory, Wiley, New York.

    • Hopfield, J.J. (1982). Neural network and physical system with emergent collective computational capabilities. In proceeding of the National Academy of Science (USA) ,79, 2554-2558.

    • Kaastra, I. and Boyd, M.(1996): Designing a neural network for forecasting financial and economic time series. Neurocomputing, 10(3), 215-236.

    • Masters, T. (1993). Practical Neural Network Recipes in C++, San Diego, Academic Press.

    • Rosenblatt, F. (1958). The perceptron: A probabilistic model for information storage and organization in the brain. Psychological review, 65, 386-408.

    • Rumelhart, D.E., Hinton, G.E., and Williams, R.J. (1986). Learning internal representations by error propagation, Nature, 323, 533-536


    • Saanzogni, Louis and Kerr, Don (2001) Milk production estimate using feed forward artificial neural networks. Computer and Electronics in Agriculture, 32, 21-30.

    • Warner, B. and Misra, M. (1996). Understanding neural networks as statistical tools. American Statistician, 50, 284-93.

    • Widrow, B. and Hoff, M.E. (1960). Adaptive switching circuit. IREWESCON convention record, 4, 96-104

    • Zhang, G., Patuwo, B. E. and Hu, M. Y. (1998). Forecasting with artificial neural networks: The state of the art. International Journal of Forecasting, 14, 35-62.


    Thank You estimate using feed forward artificial neural networks.


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