vmd-lstm预测模型代码matlab

以下是一个基于 MATLAB 的 VMD-LSTM 预测模型的代码示例：

% 加载数据
data = load('data.mat');
data = data.data;

% 划分数据集
train_ratio = 0.8;
train_size = round(train_ratio * size(data, 1));
train_data = data(1:train_size, :);
test_data = data(train_size+1:end, :);

% VMD 分解
num_modes = 8;
alpha = 2000;
tau = 0;
tol = 1e-7;
maxiter = 2000;
[V, W, ~] = VMD(train_data', alpha, tau, tol, maxiter, num_modes);

% LSTM 模型训练
input_size = num_modes;
output_size = 1;
hidden_size = 32;
num_layers = 2;
learning_rate = 0.001;
num_epochs = 100;
batch_size = 64;
train_loader = prepare_data(train_data, batch_size);
lstm_model = train_lstm(input_size, hidden_size, num_layers, output_size, learning_rate, num_epochs, train_loader);

% LSTM 模型预测
test_loader = prepare_data(test_data, 1);
lstm_predictions = predict_lstm(lstm_model, test_loader);

% VMD 重构
reconstructed_data = W * lstm_predictions;

% 可视化结果
figure;
plot(data, 'LineWidth', 2);
hold on;
plot(train_size+1:size(data, 1), reconstructed_data, 'LineWidth', 2);
legend('原始数据', '预测数据');

% 定义 VMD 函数
function [V, U, omega] = VMD(X, alpha, tau, tol, maxiter, num_modes)
    N = length(X);
    omega = zeros(N, num_modes);
    for ii = 1:num_modes
        omega(:, ii) = omega_init(N, alpha);
    end
    U = zeros(N, num_modes);
    V = X;
    K = 1;
    while K <= maxiter
        for ii = 1:num_modes
            [U(:, ii), ~] = FISTA(V, omega(:, ii), tau, tol);
        end
        u_hat = fft(U, [], 1);
        for ii = 1:num_modes
            omega(:, ii) = weight_median(u_hat(:, ii), alpha);
        end
        V_old = V;
        V = X - sum(U, 2);
        if norm(V(:) - V_old(:)) / norm(X(:)) < tol
            break;
        end
        K = K + 1;
    end
end

% 定义 FISTA 函数
function [x, obj] = FISTA(y, lambda, tau, tol)
    L = norm(y, 2)^2;
    x = y;
    t = 1;
    t_old = 1;
    for ii = 1:100
        x_old = x;
        grad = gradient(x, lambda, tau);
        x = soft_threshold(x - (1/L) * grad, 1/L);
        t_old = t;
        t = (1 + sqrt(1 + 4*t^2))/2;
        x = x + ((t_old - 1)/t) * (x - x_old);
        obj = objective(x, y, lambda, tau);
        if norm(x(:) - x_old(:)) / norm(x_old(:)) < tol
            break;
        end
    end
end

% 定义梯度和目标函数
function grad = gradient(x, lambda, tau)
    grad = -fft(kernel(x)) + lambda .* fft(weight(x)) + tau .* fft(x);
end

function obj = objective(x, y, lambda, tau)
    obj = norm(kernel(x)*x - y, 2)^2/2 + lambda .* norm(weight(x), 1) + tau .* norm(x, 1);
end

% 定义阈值函数和核函数
function y = soft_threshold(x, lambda)
    y = sign(x) .* max(abs(x) - lambda, 0);
end

function K = kernel(x)
    N = length(x);
    K = zeros(N, N);
    for ii = 1:N
        for jj = 1:N
            K(ii, jj) = abs(ii - jj);
        end
    end
    K = exp(-K.^2);
end

% 定义权重函数和权重中位数函数
function w = weight(x)
    N = length(x);
    w = zeros(N, 1);
    for ii = 1:N
        w(ii) = min(ii-1, N-ii);
    end
    w = w/max(w);
end

function wm = weight_median(x, alpha)
    N = length(x);
    w = weight(x);
    wm = zeros(N, 1);
    for ii = 1:N
        indices = max(ii-alpha, 1):min(ii+alpha, N);
        wm(ii) = median(w(indices));
    end
end

% 定义 LSTM 模型相关函数
function loader = prepare_data(data, batch_size)
    num_samples = size(data, 1);
    batches = floor(num_samples / batch_size);
    X = data(1:batches*batch_size, :);
    X = reshape(X, [batch_size, batches, size(data, 2)]);
    loader = struct;
    loader.X = X;
    loader.num_samples = num_samples;
    loader.batch_size = batch_size;
    loader.batches = batches;
end

function model = train_lstm(input_size, hidden_size, num_layers, output_size, learning_rate, num_epochs, loader)
    lstm_layers = [];
    for ii = 1:num_layers
        lstm_layers = [lstm_layers, sequenceInputLayer(input_size)];
        lstm_layers = [lstm_layers, lstmLayer(hidden_size, 'OutputMode', 'last')];
    end
    lstm_layers = [lstm_layers, fullyConnectedLayer(output_size)];
    lstm_layers = [lstm_layers, regressionLayer];
    options = trainingOptions('adam', ...
        'MaxEpochs', num_epochs, ...
        'LearnRateSchedule', 'piecewise', ...
        'LearnRateDropPeriod', 50, ...
        'LearnRateDropFactor', 0.2, ...
        'InitialLearnRate', learning_rate, ...
        'MiniBatchSize', loader.batch_size);
    X = loader.X(:, 1:end-1, :);
    Y = loader.X(:, 2:end, :);
    model = trainNetwork(X, Y, lstm_layers, options);
end

function predictions = predict_lstm(model, loader)
    predictions = zeros(loader.num_samples - loader.batch_size, 1);
    for ii = 1:loader.batches
        X_batch = loader.X(:, ii, :);
        Y_batch = model.predict(X_batch);
        predictions((ii-1)*loader.batch_size+1:ii*loader.batch_size) = Y_batch(1:end-1);
    end
end

需要注意的是，以上代码仅为示例，实际使用时需要根据具体需求进行修改和调整。此外，代码中使用了 VMD 和 FISTA 算法，需要提前安装对应的 MATLAB 工具箱。