NeuroFuzzy systems

FuNNy A compiler: FuNNy language to C. Beside the Fuzzy system, the compiler generate a simple test program that can be used as a proto-type for interfacing. A C library contains the learning algorithm: A gradient descend method based on a numerical calculation of the gradient. A random search method. Simulated annealing by combining gradient descend method and random search

tout: input; vout: input; dtcold: input; dthot: input; cold tout: sigmoid( 25.0,a, 33.0,a, 1.0,c); middle tout: triangle(28.0,a, 33.0,c, 38.0,a, 1.0,c); hot tout: sigmoid( 40.0,a, 33.0,a, 1.0,c); to_little vout: sigmoid( 1.0,c, 5.0,c, 1.0,c); to_much vout: sigmoid( 5.0,c, 1.0,c, 1.0,c); down dtcold: sigmoid(-5.0,a, 0.0,a, 1.0,c); up dtcold: sigmoid( 5.0,a, 0.0,a, 1.0,c); down dthot: sigmoid(-5.0,a, 0.0,a, 1.0,c); up dthot: sigmoid( 5.0,a, 0.0,a, 1.0,c); big_down dvc: output(-0.5,a); small_down dvc: output(-0.2,a); no_change dvc: output( 0.0,c); small_up dvc: output( 0.2,a); big_up dvc: output( 0.5,a); ---- A small example: The shower controller. ----

Simple Neuron-Fuzzy Tool for Small Control Devices

Simple Neuron-Fuzzy Tool for Small Control Devices.

Simple Neuron-Fuzzy Tool for Small Control Devices. Learning Gradient-descent based on numerical calculation of the gradient. (NG-learning)}

Initiation:  = 0.01 Increase  with 1% if  P decreases over two epochs. Decrease  with 0.5% if  P increase. Simple Neuron-Fuzzy Tool for Small Control Devices. Learning For all input/desired-outout and all parameter and many epochs do: For each input/desired-outout (i) and for each parameter (j) do.

FuNNy Controller Process v c,v h t c,t h t o,v o Simple model FuNNy controller - + t oref,v oref

Simple Neuron-Fuzzy Tool for Small Control Devices.

cold tout:sigmoid( 25.03,a, 33.19,a, 1.0,c ); middle tout:triangle(28.01,a, 33.00,c, 37.95,a, 1.0,c ); hot tout:sigmoid( 39.92,a, 32.74,a, 1.0,c ); big_down dvc: output(-0.62,a ); small_down dvc: output(-0.76,a ); no_change dvc: output( 0.00,c ); small_up dvc: output( 0.77,a ); big_up dvc: output( 0.84,a ); big_down dvh: output(-0.81,a ); small_down dvh: output(-0.76,a ); no_change dvh: output( 0.00,c ); small_up dvh: output( 0.76,a ); big_up dvh: output( 0.65,a ); Simple Neuron-Fuzzy Tool for Small Control Devices.

Rule optimaization Where to put the rules. Clostering algorithm – Kohonens self-organizing feature map.

Kohonens self-organizing feature map 1.Distribute the cluster center randomly over the input area. 2.Take the next input vector. 3.Find the nearest cluster. 4.Move the nearest cluster center a small step towards the input. 5.Go to 2 until all cluster center is steady.

Hard C-means clustering

Fuzzy C-means clustering

ANFIS: Artificial Neuro-Fuzzy Inference Systems ANFIS are a class of adaptive networks that are functionally equivalent to fuzzy inference systems. ANFIS First order Sugeno fuzzy models. If x is A1 and y is B1, then z = p1x + q1y + r1 If x is A2 and y is B2, then z = p2x + q2y + r2 A1 A2 B1 B2 Prod F1 F2 Agg x y x y + z

ANFIS model structure fis = genfis1(data, [3 7], char('pimf','trimf'));

ANFIS epoch_n = 20; out_fis = anfis(data,fis,epoch_n); Where data is a matrix with N+1 columns - first N columns contain the inputs and last column contains the output.

ANFIS learning A1 A2 B1 B2 P P P P F1 F2 A A x y x y Premise parameters If x is A1 and y is B1, then F1 = p 1 x + q 1 y + r 1 Consequent paramaters Least-squares method; Gradient decent +