How can I use SVM regression to predict power production

Hi!

I have an SVM program for predicting a day ahead power production of a solar power plant. My inputs are solar irradiance, mean temperature, Pressure and the previous day power generated. i used to 2 years data for the site (2014 & 2015) to train the model. However, even while training the model, the errors appear to be very high using both linear and kernel functions. another problem I have is that when I plot the graph, all the actual values turn zero. Attached are the screenshots of the rmse and how the graph looks. What can I do?

My code is

% Initailization

clear all;clc;

% Normalization

data= csvread('traindaily 14-15.csv');

% Input -> x, Output -> y

x=data(:,2:end-1);

y=data(:,end);

% Number of data points

N= length(data);

alpha=zeros(N,1);

% Tolerence value

norm1=10e2; tol=0.2;

% Maximum number of iterations

itr=0; itrmax=10e2;

eps=0.1;

%% linear kernel

for i = 1:N

for j = 1:N

kernel = (x(i))' .* x(i);

end

end

%% algorithm

while (norm1>tol && itr < itrmax)

alpha_ = alpha;

alpha = alpha;

for i = 1: N

alpha(i)=alpha(i) + y(i) -eps*sign(alpha(i))*kernel;

if alpha_(i)*alpha(i)<0

alpha(i)=0;

end

end

norm1=norm(alpha_-alpha);

itr=itr+1;

end

fprintf('Total number of iteration = %d',itr)

%% weight and bias

% Weights

w=sum(alpha.*x)

% Bias

b=mean(y-(w*x')' -eps*ones(N,1))

%% predicted values

% Predicted values

for j=1:N

fx1(j,:)=alpha(j)*kernel;

end

fx=sum(fx1)';

disp('[Actual Values Predicted Values]')

disp([y(1:10) ,fx1(1:10)])

% Mean Square error

rmse =sqrt(norm(y-fx1)^2/N)

%% visualization

% Plotting

figure

scatter(data(:,1),y)

hold on

scatter(data(:,1),fx1,'*')

hold off

xlabel({'X_1'});

ylabel({'X_2'});

legend1 = legend('Actual Values','Predicted Values');

Answer 1

[Jaimin]

Hi @Aisha Sa'ad

The provided SVM implementation has issues that may contribute to high errors and plotting problems. The kernel calculation seems incorrect; it is expected to involve both data points for a linear kernel. Additionally, the update for the alpha values is not properly implemented, as it typically involves the gradient of the loss function. It is advisable to use MATLAB's built-in “fitcsvm” function, which efficiently handles these complexities and optimizes the training process.

Kindly refer to a following code snippet for understanding.

% Example SVM Regression Script for Solar Power Prediction

numDays = 100;
rng(0); % For reproducibility

% Generate random features: [Solar Irradiance, Mean Temperature, Pressure, Previous Day Power]
solarIrradiance = rand(numDays, 1) * 1000; % in W/m^2
meanTemperature = rand(numDays, 1) * 35; % in °C
pressure = rand(numDays, 1) * 10 + 1000; % in hPa
previousDayPower = rand(numDays, 1) * 100; % in kWh

% Generate target variable: Power Output
powerOutput = 0.5 * solarIrradiance + 0.3 * meanTemperature + ...
              0.1 * pressure + 0.6 * previousDayPower + randn(numDays, 1) * 10;

% Combine features into a matrix
X = [solarIrradiance, meanTemperature, pressure, previousDayPower];
y = powerOutput;

% Split data into training and testing sets
trainRatio = 0.8;
numTrain = floor(trainRatio * numDays);
X_train = X(1:numTrain, :);
y_train = y(1:numTrain);
X_test = X(numTrain+1:end, :);
y_test = y(numTrain+1:end);

% Train SVM regression model
svmModel = fitrsvm(X_train, y_train, 'KernelFunction', 'linear');

% Predict on test data
predictedValues = predict(svmModel, X_test);

% Calculate RMSE for test data
rmse = sqrt(mean((y_test - predictedValues).^2));
fprintf('Test RMSE: %.2f\n', rmse);

figure;
scatter(1:numTrain, y_train, 'b', 'DisplayName', 'Training Data');
hold on;
scatter(numTrain+1:numDays, y_test, 'g', 'DisplayName', 'Test Data');
scatter(numTrain+1:numDays, predictedValues, 'r*', 'DisplayName', 'Predicted Values');
hold off;
xlabel('Day');
ylabel('Power Output (kWh)');
legend('show');
title('Actual vs Predicted Power Output');

For more information kindly refer to the following MathWorks documentation.

fitrsvm: https://www.mathworks.com/help/stats/fitrsvm.html