An analysis of low power testing using K -means clustering with reordering approach

K -means clustering is a machine learning algorithm used to group the data based on the similarity between the data. Functional distances like squared Euclidean distance, city block, cosine, correlation and ham- ming are considered as a similarity parameter here. Test vectors are grouped based on the functional distance using the K -means algorithm. A simple reordering algorithm is proposed and is applied to each group of data before ‘X’ bit ﬁling to minimize the test power. Experimental re- sults on ISCAS 89 benchmark circuit shows that the proposed methods diminish the power effectively.


Introduction:
The integrated circuit (IC) industries evolve from lowscale integration to ultra-large-scale integration. According to Morse law, every 18 months, the number of transistors in an IC gets doubled. It increases the complexity in IC design and test. Testing of an IC requires effective test patterns. Automatic test equipment (ATE) is mainly intended to predict the functionality of the integrated circuits. The test patterns are compressed and stored in ATE memory. During testing, ATE decompresses the test data to test the IC.
The test vectors have many don't care bits that should be effectively filled with logical values of '0' or '1'; otherwise, increase the switching activity between the test data and cause more power dissipation during testing. This article mainly focuses on reducing the scan in peak test power and the scan in average test power.
Low power testing challenges mainly depend on the effective filling of don't care bits in the test data. Don't care bits take more significant proportionality than other logical bits in the test set. Specific circuits, don't care bits, occupy two third of the total test bits. Filling the don't care bits plays a vital role in low power testing. Some of the existing approaches are random filling, adjacent filling and column wise bit filling (CBF). Ineffective filling increases the logical transition which leads to more dynamic power consumption. Higher power consumption may damage the IC. Identification of test vectors that cause more power dissipation is vital, and it depends on the effective don't care bit filling technique. This article uses machine learning techniques for the classification of the test set.
The other challenge in low power testing is reordering the test vectors in the test set. Hamming distance-based reordering and 2D reordering techniques are the existing methods focused on test vectors in the test set only. In Double hamming distance-based 2D reordering, two dimensions of the test set (rows and columns) are considered for reordering the test vectors for effective compression [1]. Sokal and Sneath similarity coefficient is used for reordering the test set to improve the compression [2]. Weighted transition and hamming distance-based reordering were introduced by US Mehta [3][4][5]7]. Functional distance-based test vector reordering was proposed in the year 2017 [6]. All existing methods directly use the test data for 'X' bit filling [11]. Existing methods do not effectively reduce the test power, and primarily the power results are compared with compressed test sets only.
K-means clustering with the reordering algorithm is proposed in this article [8]. It is used to cluster the test data into different groups based on various distance parameters. Bit filling is done separately for each group to effectively increase the frequency of logical bits in the test data. It further helps to reduce the logical transitions and improve the power reduction in the test data.
Proposed Work: A machine learning technique is proposed for grouping the test vectors. K-means clustering is a prominently used clustering in many applications. It groups the input data based on a certain similarity between them. The group is called a cluster. In IC testing, it is necessary to group the test data based on similarity to minimize the test power. To obtain a low power test set, it needs to identify the test data based on similarity. Initially, K (an integer) random cluster centroid has been defined by the algorithm. It assigns each test data to a cluster based on the minimal distance from the test data point to the mean of its assigned cluster. It is an iterative process till the cluster centre is not changed. The distance between the test data and the centroid can be chosen as city block, squared Euclidean distance, cosine, correlation, and hamming. Based on the distance, the test sets are classified. In this article, two initial cluster centres (K = 2) are used.
The algorithm returns an index of each test data that belongs to the specific cluster. Index value 0 indicates the first cluster, and index value 1 represents the second cluster. K-means clustering algorithm is explained as follows.
Step 1: Cluster centres are chosen randomly Step 2: Calculate the distance from the cluster centre to each test data in the test set Step 3: Assign test data to the closest cluster centre Step 4: Update the cluster centre repeatedly based on the mean of all test data that belongs to a specific cluster centre CK Step 5: Replicate steps 2 to 4 till the cluster centre is stable The mathematical expression for K-means clustering is represented as Don'T Care Bit Filling: Don't care bits are the significant source of power consumption. The logical values should be used to replace the don't care bits. The adjacent filling technique is used in this article to replace the don't care bits. It increases the runs of logic '0' and '1's. Also, the reduction of switching activity leads to a reduction in power during the IC test.
The proposed method reduces the test power effectively compared to the existing methods. Peak power and average power is calculated based on weighted transition metric. They can be represented as follows, Weightedtransition metric (WTM): Average power: Peak power:   So similarity between test vectors is lost in this approach. The proposed method utilizes K-means clustering to find the similarity between test vectors. To find the similarity, distance parameters like squared Euclidean distance, city block, cosine, correlation, and hamming are considered.
K-means using squared Euclidean distance and city block groups the test data based on the minimum distance between successive test vectors. Correlation-based clustering uses the linear relationship between successive test vectors. Hamming distance compares the positional bits of test vectors in the test set. Cosine distance measure uses the cosine angle between two test data to measure the cosine similarity. K-means clustering groups the test data based on the above-mentioned distance parameter.
K-means clustering approach is an iterative process and repeats the iteration until the mean distance between cluster centre and test data points becomes stable. So the similarity between the test vectors in the same cluster increases. This helps to improve the effective filling of don't care bits for test power reduction. Even though the hamming distance parameter is similar in the existing and proposed method, the proposed method improves the average test power and peak test power by 88% and 35%, respectively, compared to the existing 2D reordering method [1].
Not only hamming distance, the other distance parameters like squared Euclidean distance, city block, cosine, correlation also improves the similarity between test vectors that further helps to reduce the power.
Experimental work is carried out on ISCAS benchmark circuits as shown in Table 1. Results show that the proposed one effectively reduces the test power. Table 2 indicates the power details of existing methods.
The results of the proposed methods are specified in Table 3a,b. The power reduction analysis is elaborated in Table 4a,b. The observation from the results indicates that test vector classification using Kmeans clustering with functional distances and reordering reduces the test power effectively than the existing methods.
Conclusion: In this article, the K-means clustering algorithm is used to group the test vectors in the test set based on functional distances like squared Euclidean distance, city block, cosine, correlation and hamming. The test vector reordering based on the test vectors' positional weights further helps to increase the runs of logical values in the test set. The experimental result shows that the proposed one effectively reduces both scan in peak and average test power. The power reduction analysis in Table 4a,b shows that correlation-based similarity measure with re-ordering effectively reduces the test power than other function distance parameters.