Advanced Process Control Using Partial Least Squares

2012 ◽  
Vol 542-543 ◽  
pp. 124-127
Author(s):  
Shu Kai S. Fan ◽  
Yuan Jung Chang
Keyword(s):  
Process Control ◽  
Least Squares ◽  
Partial Least Squares ◽  
Model Building ◽  
Moving Average ◽  
Multiple Input Multiple Output ◽  
Advanced Process Control ◽  
Virtual Metrology ◽  
Multiple Input ◽  
Input Multiple Output

This paper applies the partial least squares (PLS) technique to the multiple-input multiple-output (MIMO) semiconductor processes under the paradigm of the Advanced Process Control (APC). First, we present a controller called the PLS-MIMO double exponentially weighted moving average (PLS-MIMO DEWMA) controller. It uses the PLS method as the model building/estimation technique to help the EWMA controller to produce more consistent and robust control outputs than purely using the conventional EWMA controller. To cope with metrology delays, the proposed controller uses the pre-process metrology data to build up a Virtual Metrology (VM) system that can provide the estimated process outputs for the PLS-MIMO DEWMA controller. Finally, a Fault Detection (FD) system is added based upon the principal components of PLS, which supplies the process state for VM and the PLS-MIMO DEWMA controller to respond to the system errors.

AN ANALYSIS AND MIMO EXTENSION OF A DOUBLE EWMA RUN-TO-RUN CONTROLLER FOR NON-SQUARED SYSTEMS

2003 ◽  
Vol 10 (04) ◽  
pp. 417-428 ◽  
Author(s):  
RAMKUMAR RAJAGOPAL ◽  
ENRIQUE DEL CASTILLO
Keyword(s):  
Semiconductor Manufacturing ◽  
Control Method ◽  
Moving Average ◽  
Multiple Input Multiple Output ◽  
Processing Step ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Average Control ◽  
Controllable Factor ◽  
Weighted Moving Average

The double EWMA (exponentially weighted moving average) control method is a popular algorithm for adjusting a process from run to run in semiconductor manufacturing. Until recently, the dEWMA controller had been applied only for the single controllable factor (or input), single quality charcteristic (or output) case. Recently, Del Castillo and Rajagopal4 propose a multivariate double EWMA controller for squared multiple-input, multiple-output (MIMO) processes, where there is an equal number of inputs and outputs. This paper extends the MIMO dEWMA controller for non-squared systems. Two different MIMO dEWMA controllers are presented and their performance studied with application to a Chemical-Mechanical Polishing (CMP) process, a critical semiconductor manufacture processing step that exhibits non-linear dynamics.

scholarly journals Identifikasi Amplitudo dan Sudut Kedatangan Sinyal Menggunakan Metode Forward-Backward APES pada Radar Multi-Antena

2021 ◽  
Vol 7 (2) ◽  
pp. 89-99
Author(s):  
Sapriansa Sapriansa ◽  
Syahfrizal Tahcfulloh
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Cross Section ◽  
Phased Array ◽  
Multiple Input Multiple Output ◽  
Radar Cross Section ◽  
Phase Estimation ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Ls Estimator

Jenis sistem radar multi-antena ada dua macam yaitu phased-array (PA) dan Multiple-input Multiple-Output (MIMO). Parameter yang digunakan untuk menguji kinerja radar PA dan MIMO ada banyak sekali yang salah satunya adalah estimasi parameter yang berkaitan dengan jumlah target deteksi. Estimasi parameter termasuk di dalamnya yaitu sudut kedatangan sinyal (direction of arrival, DoA) dan amplitudo sinyal pantulan. Penelitian ini mengusulkan perluasan dari pendekatan estimasi parameter yaitu amplitudo and phase estimation (APES) yang dinamakan forward-backward APES (FBAPES). Pendekatan ini memberikan perbaikan resolusi terhadap estimasi amplitudo dan DoA dari sinyal pantulan target radar yang dikomparasikan dengan estimator konvensional seperti least squares (LS). Formulasi dan evaluasi kinerja estimator yang diusulkan akan diuji berdasarkan berbagai faktor seperti besar radar cross section (RCS), resolusi sudut antar dua target, dan jumlah elemen antena di transmitter-receiver (Tx-Rx). Resolusi sudut deteksi yang diperoleh untuk estimator ini lebih baik dari estimator LS, sebagai contoh untuk M = N = 8 maka diperoleh resolusi sudut 3o sedangkan estimator LS sebesar 5,8o. There are two types of multi-antenna radar systems, i.e. the phased-array (PA) and the multiple-input multiple-output (MIMO). There are many parameters used to test the performance of the PA and the MIMO radars, one of which is parameter estimation related to the number of detection targets. Estimated parameters include the angle of arrival of the signal (direction of arrival, DoA) and the amplitude of the reflected signal. This study proposes an extension of the parameter estimation approach, namely amplitude and phase estimation (APES), which is called forward-backward APES (FBAPES). This approach provides improved resolution of the amplitude and DoA estimates of the reflected radar target signal compared to conventional estimators such as least squares (LS). The formulation and evaluation of the performance of the proposed estimator will be carried out based on various factors such as variations in radar cross section (RCS), angular resolution between two targets, and the number of antenna elements in the transmitter-receiver (Tx-Rx). The resolution of the detection angle obtained for this estimator is better than the LS estimator, for example for M = N = 8 then the angle resolution is 3o while the LS estimator is 5.8o.

scholarly journals Схема оценивания канала для систем связи MIMO с помощью методов обобщенного разложения Холецкого и обратной подстановки

2021 ◽  
Vol 64 (6) ◽  
pp. 374-379
Author(s):  
П. Саксена ◽  
С. Б. Патель ◽  
Дж. К. Бхалани
Keyword(s):  
Independent Component Analysis ◽  
Least Squares ◽  
Multiple Input Multiple Output ◽  
Cholesky Decomposition ◽  
Component Analysis ◽  
Independent Component ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Maximum A Posterior

В статье исследована и реализована новая схема полуслепого оценивания канала для системы связи MIMO (Multiple-Input Multiple-Output) для случая канала с квазистатическим рэлеевским замиранием. В этой схеме канальная матрица H остается относительно постоянной в пределах блока. Канальную матрицу H можно разложить на матрицу вращения Q и нижнюю треугольную матрицу R. Треугольная матрица R оценивается вслепую при использовании метода обобщенного разложения Холецкого GCD (generalized Cholesky decomposition) на основе QR-разложения выходной ковариационной матрицы, которая использует стохастический метод слепого разделения входных сигналов на основе анализа независимых компонентов ICA (Independent Component Analysis). Матрица Q оценивается по ортогональным пилотным символам при использовании нового подхода, основанного на QR-разложении, для минимизации целевой функции. При использовании этого нового подхода ортогональные пилотные символы можно разложить на детерминированную эрмитову матрицу и верхнюю треугольную матрицу, используя QR-разложение. Наконец, матрицу Q можно оценить, используя метод обратной подстановки, который представлен в данной работе. Проведено моделирование при использовании двух передающих антенн с пространственно-временным кодом Аламоути и комбинаций из 2 и 6 приемных антенн, чтобы исследовать эффективность работы новой схемы оценивания по сравнению со стандартными схемами оценивания на базе методов наименьших квадратов LS (Least Squares) и максимальной апостериорной оценки MAP (Maximum a posterior) при использовании схемы модуляции данных BPSK (двоичная фазовая манипуляция). Полученные результаты показали, что новая схема превосходит по эффективности работы другие схемы и демонстрирует значительно лучший результат в отношении характеристики коэффициента битовых ошибок BER. Таким образом, новая схема может быть весьма полезной для решения сложной задачи полуслепого оценивания канала MIMO с помощью метода QR-разложения матрицы. Кроме того, представлен анализ ошибок в терминах матрицы ковариации ошибки при рассмотрении шума для случая ненулевой ошибки (практический случай) по сравнению со случаем нулевой ошибки.

scholarly journals Using Machine Learning Classifiers to Recognize the Mixture Control Chart Patterns for a Multiple-Input Multiple-Output Process

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 102 ◽  
Author(s):  
Yuehjen E. Shao ◽  
Yu-Ting Hu
Keyword(s):  
Machine Learning ◽  
Process Control ◽  
Control Chart ◽  
Mimo Systems ◽  
Multiple Input Multiple Output ◽  
Multivariate Adaptive Regression Splines ◽  
Support Vector ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Control Chart Pattern

A statistical process control (SPC) chart is one of the most important techniques for monitoring a process. Typically, a certain root cause or a disturbance in a process would result in the presence of a systematic control chart pattern (CCP). Consequently, the effective recognition of CCPs has received considerable attention in recent years for their potential use in improving process quality. However, most studies have focused on the recognition of CCPs for SPC applications alone. Specifically, even though numerous studies have addressed the increased use of the SPC and engineering process control (EPC) mechanisms, very little research has discussed the recognition of CCPs for multiple-input multiple-output (MIMO) systems. It is much more difficult to recognize the CCPs of an MIMO system since two or more disturbances are simultaneously involved in the process. The purpose of this study is thus to propose several machine learning (ML) classifiers to overcome the difficulties in recognizing CCPs in MIMO systems. Because of their efficient and fast algorithms and effective classification performance, the considered ML classifiers include an artificial neural network (ANN), support vector machine (SVM), extreme learning machine (ELM), and multivariate adaptive regression splines (MARS). Furthermore, one problem may arise due to the existence of embedded mixture CCPs (MCCPs) in MIMO systems. In contrast to using typical process outputs alone in a classifier, this study employs both process outputs and EPC compensation to ensure the effectiveness of CCP recognition. Experimental results reveal that the proposed classifiers are able to effectively recognize MCCPs for MIMO systems.

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